We present the design and performance of RoboPol, a four-channel optical polarimeter operating at the Skinakas Observatory in Crete, Greece. RoboPol is capable of measuring both relative linear Stokes parameters q and u (and the total intensity I) in one sky exposure. Though primarily used to measure the polarization of point sources in the R band, the instrument features additional filters (B, V, and I), enabling multiwavelength imaging polarimetry over a large field of view (13.6' × 13.6'). We demonstrate the accuracy and stability of the instrument throughout its 5 yr of operation. Best performance is achieved within the central region of the field of view and in the R band. For such measurements the systematic uncertainty is below 0.1 per cent in fractional linear polarization, p (0.05 per cent maximum likelihood). Throughout all observing seasons the instrumental polarization varies within 0.1 per cent in p and within ˜1° in polarization angle.