A fault is observed in a road cut, but there are no obvious rocks units to correlate on either side of the fault to determine relative movement

The fault is normal if the hanging wall is moving down. This type of fault is caused by extensional forces, and forms horst and graben. If you are in the Basin and Range province, you are likely dealing with a normal fault.

A reverse fault is due to compressional forces, which cause the hanging wall to move upward relative to the footwall. If you are near a subduction zone, you are likely dealing with this type of fault.

You could also analyze the fossils appearing on each side of the fault. The more recent species will be above more ancient ones. Therefore, at the same elevation, you can compare the fossil assembleges on the footwall and the hanging wall to determine relative movement.

Absolute dating by means of radioactive decay can also be used in the same manner as fossils to determine relative movement.