Is it common to have a mentor in academia?
I won't try to guess how common it is, suspecting that it is quite common. But it is very useful in any case. 

But there are two (at least) scenarios. 

The first is that your "mentor" doesn't even know that s/he is your mentor, but you just take cues from them about how to behave in any academic and personal situations that you observe. How do they lecture? How do they respond to questions? How do they interact with colleagues. I've had many mentors of this kind. I was lucky enough to meet up with one of the most important ones later and thanked him for providing the role-model I needed as an academic. He was in the same field, but his research area was very different from mine. 

The second is more personal. This is someone that you specifically interact with, though not necessarily in a research sense. But someone that you are comfortable asking questions of. Even somewhat uncomfortable questions. Someone who you trust will give you good feedback and not be shocked it you ask a strange question that you might not ask a stranger. These relationships are harder to arrange and must, IMO, develop over time. 

The second sort of "formal" mentor can be more instrumental in promoting your career, of course, since they know you well and, having taken on the role, are likely to be supportive when asked. 

If you are a grad student, I strongly suggest that you seek out one or more professionals as mentors of either kind. Even better, is to seek out a circle of people who are mutually supportive - but for the right reasons. People who respect one another and help when they can.