Well, there are several hymns in Vedas which can mention rebirth.
However it depends upon interpretation .
I've found couple of verses from Rigveda Mandala 1 of which interpretation mention rebirth according to Swami Dayananda Sarasvati, the founder of Arya Samaj.
Though Ralph Griffith or Gayatri Pariwar's translation doesn't mention rebirth.
Quoting Rigveda Bhashya of Swami Dayananda Saraswati : English translation : PURPORT
In this Mantra, the doctrine of Re-birth is enunciated.
Whatever kind of actions performed by men, they got the same kind of birth and enjoyment in the next Rigveda Mandala 1, Sukta 24, Mantra 2: English Translation: PURPORT:
O men, we certainly believe in om
eternal, Immortal God who is dispense of fruit of good or bad actions done by us and according to Whose laws we get rebirth .
You must also know that one God to be giver of rebirth , non else can do this work.
It is he who gives birth to emancipated persons also through parents at the end of MahaKalpa.
hinduism.stackexchange.com/users/277/Pandya
RV mentions reincarnation in mandala X hymn 56, however the notion of reincarnation is different from as we know it today.
After a person dies his soul starts journey to some unknown world.
Then the Gods transfer his soul to their domain and unites the soul with body.
So the notion is similar to what ancient Egyptians had where after death soul unites with body and the person starts enjoying life again after being dead!
hinduism.stackexchange.com/users/None/
Yes.
Shukla Yajurveda Book III
We call the spirit hither with a hero-celebrating strain, Yea, withthe Fathers’ holy hymns (53)
The spirit comes to us again for wisdom,energy, and life, That we may long behold the Sun (54) The spirit here denotes Atma which comes to us (human beings) after being somewhere for sometimes.
Since it is clearly written that it comes again, it clearly denote reincarnation.
Atharva Veda IX.10 Back
, forward goes he, grasped by power inherent, immortal born thebrother of the mortal.
Ceaseless they move in opposite directions:
menmark the one and fail to mark the other (16)
The he mentioned here
is Atma which is immortal and the mortal here is body.
What this verse says is that there is no time frame for reincarnation.
It also says men will notice only one thing (mortal body) and fail to notice the other (Atman).
Rig
Veda X.16 Burn him not up, nor quite consume him, Agni: let not his body or hisskin be scattered.
O Jātavedas, when thou hast matured him, thensend him on his way unto the Fathers .
(1)
When thou hast made him ready, Jātavedas, then do thou give him overto the Fathers.
When he attains unto the life that waits him, he shallbecome the Deities' controller.
(2)
These verses pray to Agni to send the spirit of the dead person to forefathers once the body is perfectly burned up.
The Sun receive thine eye, the Wind
thy spirit; go, as thy merit is,to earth or heaven.
Go, if it be thy lot, unto the waters; go, makethine home in plants with all thy members.(3)
The merit mentioned here is Karma.
What this verse says is that based on the merit, the spirit of the dead person go to earth (to be born as human) or heaven or waters.
( I don't know what the waters here signify)
Again, O Agni, to the Fathers send him who, offered in thee, goes withour oblations.
Wearing new life let him increase his offspring: lethim rejoin a body , Jātavedas.
(5)
This verse asks Agni to send the dead person to forefathers(Pitrus) through the oblations or last rites done by some people.
Also the second sentence clearly says he may be reborn by joining a body and increase his offspring.
hinduism.stackexchange.com/users/16083/Spark Sunshine
There is no explicit mention of reincarnation in the Vedic Samhitas.
However, some people think that some verses in the Vedic Samhitas can be interpreted to mean reincarnation.
I have heard the mention of two pathways, of birth and death, the ways of parents, the learned and the mortals.
On these two roads each moving creature travels.
Each soul leaves the present parents and assumes new ones.
Yajur Veda 19.47 translated by Devi Chand
hinduism.stackexchange.com/users/121/Pradip Gangopadhyay
There are no explicit mention
but there are mention of puranas in hymns of vedas and puranas in turn mention rebirth so- Verses, and songs,and magic hymns,purana,sacrificial text.all the celestial Gods whose home is heaven sprang from the residue.(Atharva Veda book 11,hymn 7 verse 24). Furthermore-
Lord vishnu's vamana avatar is mentioned in samhitas, the three gunas are mentioned in atharva veda- if there is mention of avatars in Vedas like vamana- sage narayana then it will support rebirth too.
The samhitas are part of upasana and devata kanda finding karma and rebirth in them is impossible.
Brahmanas are karma kanda
you won't find them mentioning rebirth or other such philosophy.
Each part of veda is for different reason.
Brahmanas is for rituals.
hinduism.stackexchange.com/users/15112/Anisha
Reincarnation is a concept of Hinduism mentioned in the Upanishads, Puranas, Bhagavad Gita, but I could not find its mention in the Veda Samhitas.  Is it mentioned in the four Vedas, that is in the Vedic Samhitas: Rig Veda, Yajur Veda, Sama Veda or the Atharva Veda?
Is reincarnation or rebirth mentioned in the Vedas (Samhitas)?
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<vedas><rebirth><samhita>
hinduism.stackexchange.com/questions/21502
hinduism.stackexchange.com/users/11510/Karmanya Nanda
There are a couple of verses from Rigveda Mandala 1 of which interpretation mention rebirth according to Swami Dayananda Sarasvati, the founder of Arya Samaj and there is  Shukla Yajurveda Book III. However, There is no explicit mention of reincarnation in the Vedic Samhitas. Some say there is no explicit mention of reincarnation in the Vedic Samhitas. However, some maintain that reincarnation is mentioned in Shukla Yajurveda Book III, Rigveda Mandala 1 as well as in several hymns in Vedas.
There is no explicit mention of reincarnation in the Vedic Samhitas. Reincarnation is said to be mentioned in Shukla Yajurveda Book III, Rigveda Mandala 1 as well as in several hymns in Vedas. 