If Tobi could use the izanagi, which requires both Senju and Uchiha DNA, then why wasn’t he able to awaken the Rinnegan on his own? It was stated by Tobi during his fight with Konan that Izanagi can only be used by those with both the DNA of Senju and Uchiha. We also know this is how the rinnegan is awakened, so why didn’t this happen?
Tobi was not able to awaken the Rinnegan despite having both Uchiha and Senju DNA because he was missing a certain step in the evolution, and that is, the Eternal Mangekyo Sharingan.


   (I slightly explained obito's case in one of my previous answers)


The evolution of the Sharingan involves firstly awakening the Mangekyo, then after a combination with another family members Mangekyo, it evolves to an Eternal mangekyo sharingan, after which adding Senju DNA to the mix awakens the Rinnegan. 

Tobi's Sharingan never reached the EMS and so thats why even tho he had combined both Uchiha and Senju DNA, he still was not able to awaken the Rinnegan.