How many times has someone taken birth into samsara? According to dependent origination I took birth (i.e I came into existence) due to ignorance. 

My questions are :how many times it has happened that someone has taken birth into this samsara? 

Since when birth of ignorance has been happening?

If there are no answers in the scriptures to the above questions then what is your personal opinion on the issues mentioned above?
According to the Assu Sutta:


  There the Blessed One said: "From an inconstruable beginning comes
  transmigration. A beginning point is not evident, though beings
  hindered by ignorance and fettered by craving are transmigrating &amp;
  wandering on. What do you think, monks: Which is greater, the tears
  you have shed while transmigrating &amp; wandering this long, long time —
  crying &amp; weeping from being joined with what is displeasing, being
  separated from what is pleasing — or the water in the four great
  oceans?"
  
  "As we understand the Dhamma taught to us by the Blessed One, this is
  the greater: the tears we have shed while transmigrating &amp; wandering
  this long, long time — crying &amp; weeping from being joined with what is
  displeasing, being separated from what is pleasing — not the water in
  the four great oceans."
  
  "Excellent, monks. Excellent. It is excellent that you thus understand
  the Dhamma taught by me.


According to this article, the total amount of tears a person sheds on average in a lifetime is estimated to be 64 litres.

According to this USGS estimation and this article, there is an estimated 1.332 billion cubic kilometers of water in the Earth's oceans. That's 1.332 x 1021 litres.

If I divide that by 64, I get 2.08125 x 1019 lifetimes.

According to the short scale, that's 20 quintillion (20 x 1018).

Hence, according to the Buddha, every person has been reborn at least 20 quintillion times.

However, since the Buddha says that "a beginning point is not evident", I guess that it should be far greater than 20 quintillion times. Maybe a googleplex amount of times.