The gravitational Aharonov-Bohm (AB) effect is examined in the weak-fi
eld a general relativity. In analogy with the electromagnetic AB effec
t, we find that a gravitoelectromagnetic 4-vector potential gives rise
to interference effects. A matter wave interferometry experiment, bas
ed on a modification of the gravity-induced quantum interference exper
iment of Colella, Overhauser and Werner (COW), is proposed to explicit
ly test the gravitoelectric version of the AB effect in a uniform grav
itational field.