In Modern Quantum Mechanics (2nd ed.) by J.J. Sakurai, in section 4.4 on 'The Time-Reversal Discrete Symmetry' he derives the time-reversal operator, \Theta, for the spin-$\frac{1}{2}$ case as (pg.: 277, eq. (4.4.65)):
\Theta = \eta e^{\frac{-i \pi S_{y}}{\hbar}}K = -i \eta \left(...