We present time-resolved photometry of the optical counterpart to the black hole candidate Swift J1753.5-0127 which has remained in the low/hard X-ray state and bright at optical/IR wavelengths since its discovery in 2005. At the time of our observations Swift J1753.5-0127 does not show a decay trend but remains stable at R=16.45 with a night-to-night variability of ~0.05 mag. The R-band light curves, taken from 2007 June 3 to August 31, are not sinusoidal, but exhibit a complex morphology with remarkable changes in shape and amplitude. The best period determination is 3.2443+/-0.0010 hr. This photometric period is likely a superhump period, slightly larger than the orbital period. Therefore, Swift J1753.5-0127 is the black hole candidate with the shortest orbital period observed to date. Our estimation of the distance is comparable to values previously published and likely places Swift J1753.5-0127 in the Galactic halo.