Answer
There is little effect. See work below.
Work Step by Step
In house wiring, very often 2 currents are being carried in opposite directions by two closely-spaced wires, whose magnetic fields tend to cancel each other.
Furthermore, the currents in a house circuit oscillate at either 50 or 60 Hz (AC current), so the magnetic fields they create oscillates at that frequency as well.
Due to the inertia of the compass needle, it doesn’t track the magnetic field changing direction so frequently, so the compass probably won’t be affected much by AC magnetic fields.
