We show that an electrical shift current is generated when electrons are ph
otoexcited from the valence to conduction bands on a BN nanotube. This phot
ocurrent follows the light pulse envelope and its symmetry is controlled by
the atomic structure of the nanotube. We find that the shift current has a
n intrinsic quantum mechanical signature in which the chiral index of the t
ube determines the direction of the current along the tube axis. We identif
y the discrete lattice effects in the tangent plane of the tube that lead t
o an azimuthal component of the shift current. The nanotube shift current c
an lend to ultrafast optoelectronic and optomechanical applications.