We calculate the toroidal quadrupole moment and form factor of the deuteron, which violate time-reversal symmetry but conserve parity, at leading order in two-flavor chiral effective field theory with perturbative pion exchange. We take into account time-reversal and parity violation due to the QCD vacuum angle combined with parity violation resulting from the weak interaction in the Standard Model. We also consider time-reversal and parity violation that at the quark-gluon level results from effective dimension-six operators originating from physics beyond the Standard Model.