  We study an integrable two-leg spin-1/2 ladder with an XYZ-type rung
interaction. Exact rung states and rung energies are obtained for the
anisotropic rung coupling in the presence of a magnetic field. Magnetic
properties are analyzed at both zero and finite temperatures via the
thermodynamic Bethe ansatz and the high-temperature expansion. According to
different couplings in the anisotropic rung interaction, there are two cases in
which a gap opens, with the ground state involving one or two components in the
absence of a magnetic field. We obtain the analytic expressions of all critical
fields for the field-induced quantum phase transitions (QPT). Anisotropic rung
interaction leads to such effects as separated magnetizations and
susceptibilities in different directions, lowered inflection points and remnant
weak variation of the magnetization after the last QPT.
