You could resolve force F to be 2 vectors one parallel to AB & one at 90 degrees. The parallel force F' can be ignored as it's just trying to stretch/compress the link AB, the other, F'', provides a turning moment around B.
sorry for the ascii graphics ;)
F' <---- A-------B
Then as you iterate your solution F'' will reduce to zero, as you rotate AB in proportion to the magnitude of F'' for each step.
It's not entirely obvious to me that the body will rotate about A, it will depend on how the external forces are applied to it. So without more information I don't know if your intuition is correct.