The collapse of slowly rotating molecular cloud cores threaded by magnetic fields is investigated by high-resolution numerical simulation. Outflow formation in the collapsing cloud cores is also followed. In the models examined, the cloud core and parent cloud rotate rigidly and are initially threaded by a uniform magnetic field. The simulations show that the cloud core collapses along the magnetic field lines. The magnetic field in the dense region of the cloud core rotates faster than that of the parent cloud as a consequence of spin-up of the central region during the collapse. The cloud core exhibits significant precession of the rotation axis, magnetic field, and disk orientation, with precession highest in the models with low initial field strength (20 G). Precession in models with initial fields of 40 G is suppressed by strong magnetic braking. Magnetic braking transfers angular momentum form the central region and acts more strongly on the component of angular momentum oriented perpendicular to the magnetic field. After the formation of an adiabatic core, outflow is ejected along the local magnetic field lines. Strong magnetic braking associated with the outflow causes the direction of angular momentum to converge with that of the local magnetic field, resulting in the convergence of the local magnetic field, angular momentum, outflow, and disk orientation by the outflow formation phase. The magnetic field of a young star is inclined at an angle of no more than 30° from that of the parent cloud at initial field strengths of 20 G, while at an initial field strength of 40 G, the magnetic field of the young star is well aligned with that of the parent cloud.