The bottom line is that, while there is nothing to stop you from trying to refinance at any time, it is generally better to wait at least a short period of time.
Wait at least 60-90 days from getting your original loan to refinance. It typically takes this long for the title on your vehicle to transfer properly, a process that will need to be completed before any lender will consider your application. Refinancing this early typically only works out for those with great credit.
Consider refinancing after six months. If you have fair to great credit, you will begin to have refinancing options after this length of time.
If you are a first-time car loan borrower, wait at least a year to refinance your loan. A first-time borrower typically needs to build up a good car loan payment history before refinancing.