We study the effect of magnetic braking due to a primordial magnetic field in the context of the formation of massive ( \gtrsim 10 ^ { 4 } M _ { \odot } ) direct collapse black holes ( DCBHs ) at high redshifts . Under the assumption of axial symmetry , we analytically compute the effect of magnetic braking on the angular momentum of gas collapsing into the potential well of massive dark matter haloes ( \simeq 10 ^ { 7 - 9 } M _ { \odot } ) which are spun up by gravitational tidal torques . We find that a primordial magnetic field of strength B _ { 0 } \simeq 0.1 nG ( comoving ) can remove the initial angular momentum gained by the in-falling gas due to tidal torques , thus significantly lowering the angular momentum barrier to the formation of DCBHs . These magnetic field strengths are consistent with the bounds on primordial fields from astrophysical and cosmological measurements and they are large enough to seed observed galactic magnetic fields .