We present the first linear polarimetric survey of white dwarfs (WDs). Our sample consists of WDs of DA and DC spectral types in the SDSS r magnitude range from 13 to 17. We performed polarimetric observations using the RoboPol polarimeter attached to the 1.3-m telescope at Skinakas Observatory. We have 74 WDs in our sample, of which almost all are low-polarized WDs with a polarization degree (PD) lower than 1 per cent; only two have a PD higher than 1 per cent. There is evidence that on average isolated DC-type WDs have a higher PD (with a median PD of 0.78 per cent) than isolated DA-type WDs (with a median PD of 0.36 per cent). On the other hand, the median PD of isolated DA-type WDs is almost the same (i.e. 0.36 per cent) as the median PD of DA-type WDs in binary systems with red dwarfs (dM type; i.e. 0.33 per cent). This shows, as expected, that there is no contribution to the PD from the companion if the WD companion is a red dwarf, which is the most common situation for WDbinary systems.We do not find differences in the PD between magnetic and non-magnetic WDs. Because 97 per cent of WDs in our sample have a PD lower than 1 per cent, they can be used as faint zero-polarized standard stars in the magnitude range from 13 to 17 of the SDSS r filter. They cover the Northern sky between 13^h and 23^h in right ascension and between -11° and 78° in declination. In addition, we found that for low extinction values (<0.04), the best model that describes the dependence of the PD on E(B - V) is given by the equation PD_max,ISM[per cent] = 0.65 E(B - V)^0.12.