Rejected an offer and then became interested (a bad decision I made) Three months ago, a professor has offered to me a research position at his university with high salary, and I rejected it because I wanted to join a master's program. Unfortunately, I made a bad decision and now I changed my mind and became very interested to the exciting position he offered to me.

Do you think is it a good idea that I send him an email and ask if the offer is still available? So even that I rejected the offer 3 months ago, is it possible that I ask the professor about that offer again?
Yes, it is a good idea to ask. But explain that you now think you made a mistake in rejecting the offer. You might also want to mention your longer term goals, which I assume include further education. He can help you with that if he has a good sense of your needs. If your work for him is good enough, he might also have some incentive to help you along. One hopes for such an outcome, anyway. 

But yes, ask. Silence gains you nothing, nor him, either.