We have obtained I-band photometry of the neutron star X-ray transient Aql X-1 during quiescence. We find a periodicity at 2.487 cycles d^-1, which we interpret as twice the orbital frequency (19.30+/-0.05 h). Folding the data on the orbital period, we model the light-curve variations as the ellipsoidal modulation of the secondary star. We determine the binary inclination to be 20 deg-30 deg (90 per cent confidence) and also determine the 95 per cent upper limits to the radial velocity semi-amplitude and rotational broadening of the secondary star to be 117 and 50 km s^-1, respectively.