  We present the design of a compact AC susceptometer for studies under
arbitrarily oriented static magnetic fields, in particular magnetic fields
oriented transverse to the AC excitation field. The small size of the
susceptometer permits versatile use in conventional cryostats with
superconducting magnet systems. The design of the susceptometer minimizes
parasitic signal contributions while providing excellent thermal anchoring
suitable for measurements in a wide range down to very low temperatures. The
performance is illustrated by means of measurements of the transverse
susceptibility at the magnetic field tuned quantum phase transition of the
dipolar-coupled Ising ferromagnet LiHoF$_4$.
