The first problem is that typical dark matter particles are moving at ~300 km/s with respect to the earth. But even if one particle was very fortunate and fell toward the earth from essentially zero relative velocity, the problem is conservation of energy. The particle would gain speed as it fell, pass through the earth, and then lose the same amount of speed on the way out of the system, escaping earth's influence again.

In principle a particle could be temporarily trapped in the earth's influence via an interaction with the moon, so that it would transfer its energy to the moon. However this still leaves it on an orbit that takes it at least as far as the moon, and it would eventually be ejected by another interaction with the moon. (This sometimes happens with solar system objects.)