The Nd-doped cuprate La_{2-y-x}Nd_ySr_xCuO_4 displays a first-order phase transition at T_d (= 74 K for x=0.10, y = 0.60) to a low-temperature tetragonal (LTT) phase. A magnetic field H applied || the a-axis leads to an increase in T_d, whereas T_d is decreased when H || c. These effects show that magnetic ordering involving both Nd and Cu spins plays a key role in driving the LTO-LTT transition. Related anisotropic effects are observed in the uniform susceptibility and the in-plane magnetoresistance.