Does Einstein's theory of relativity say that there is anyway to experimentally measure a difference between a force experienced by gravity and a force experienced by acceleration ?

Firstly, you should make sure you know the difference between special and general relativity. These are 2 different theories that Einstein helped to develop.

Secondly, in general relativity, gravity does not exert a force. So I'm not sure how to answer your question.

I think what he's asking is: when a body experiences acceleration is there any way to determine whether that acceleration is caused by gravity versus it being caused by some other external force.

I think what he's asking is: when a body experiences acceleration is there any way to determine whether that acceleration is caused by gravity versus it being caused by some other external force.

Yes, when a body experiences a force: is there anyway to experimentally determine wheather it is due to gravity or due to acceleration?

For example, if a space station is rotating (& the centifugal force "simulates" gravity), do the astronauts on the space station have any way to tell wheather they are experiencing a gravitational force or cetrifugal force?