Yes, as long as it is for an approved health problem and deemed medically necessary. This would be covered under Medicare Part B and will be paid at 80% of the approved amount. Medicare pays for any Medically necessary testing, such as blood work, X Rays, Cat Scans, and a lot of other issues. Some preventative tests are covered at 100%
A good starting point is healthcarebluebook dot com and search for MRI (or any other procedure).
Another is to "Google" Medicare DRG rates or Medicare payment schedule.