Of course you can get an MRI if you have a tattoo.
MRI stands for Magnetic Resonance Imaging. It's a big magnet.
Occasionally, especially with Jewelry, or implants, the magnetic waves
from the MRI will bounce off of metal objects. You should always remove
jewelry before getting an MRI. When the waves bounce off of certain
metals, especially Ferrous (containing Iron), they cause the metal
to move and possibly heat up.
There is generally a very low, if any, level of Iron
in any tattoo pigment. Some people have reported a slight burning
sensation, and others have noted tightness where the tattoo is. I have not
found any substantiated reports of bad imaging, severe pain, or permanent
damage. If I do, I will update. Surprisingly, the one customer I have had
reports of tightness during an MRI scan was affected by his black tribal
armband, rather than his brown eagle.
I have mentioned that Iron Oxide is present in most
commercial permanent cosmetic pigments. Permanent cosmetics are usually
not dense enough to cause these effects.