Is it possible to get the Rinnegan by injecting Senju and Uchiha DNA into yourself? Is it possible to get the Rinnegan if you are not in the Senju or Uchiha clan (including branch clans such as Uzumaki) and inject Senju and Uchiha DNA into yourself?
To awaken the Rinnegan, it's not enough to be a Senju with Uchiha eyes or vice versa, you must be Indra's successor that obtained chakra from Asura's successor.

A successor does not necessarily come directly from the Senju clan, as Naruto, who is an Uzumaki, is a successor. However, Indra's successor is always an Uchiha.

So in short, no. It's not possible to do what you describe.