  The hypothesis of the quark Reggeization is tested by taking the high-energy
limit of the two-loop amplitude for quark-gluon scattering which was recently
calculated. The limit is compatible with the Reggeization in the leading and
the next-to-leading orders and allows the determination of the quark trajectory
in the two-loop approximation. The trajectory is presented as an expansion in
powers of (D-4) for the space-time dimension $D$ tending to the physical value
D=4.
