  The ultra-strong magnetic field of magnetars modifies the neutrino cross
section due to the parity violation of the weak interaction and can induce
asymmetric propagation of neutrinos. Such an anisotropic neutrino radiation
transfers not only the linear momentum of a neutron star but also the angular
momentum, if a strong toroidal field is embedded inside the stellar interior.
As such, the hidden toroidal field implied by recent observations potentially
affects the rotational spin evolution of new-born magnetars. We analytically
solve the transport equation for neutrinos and evaluate the degree of
anisotropy that causes the magnetar to spin-up or spin-down during the early
neutrino cooling phase. Supposing that after the neutrino cooling phase the
dominant process causing the magnetar spin-down is the canonical magnetic
dipole radiation, we compare the solution with the observed present rotational
periods of anomalous X-ray pulsars 1E 1841-045 and 1E 2259+586, whose poloidal
(dipole) fields are $\sim 10^{15}$ G and $10^{14}$ G, respectively. Combining
with the supernova remnant age associated with these magnetars, the present
evaluation implies a rough constraint of global (average) toroidal field
strength at $B^\phi\lesssim 10^{15}$ G.
