Yes, you go get a loan and buy the car from the person currently on title. That's the only way to have the loan report to your credit report is to have the loan in your name.
I think you need to refinance the car. I did that. My dad and I were both on my car note and listed as co owners. In 2 and half years my credit went up and I was able to refi the loan into my name at my bank and just put my name on it at the tax office. I am not sure if it could be done without a refi.