We present the results of a VLT polarimetric monitoring campaign of the GRB 020813 optical afterglow carried out in three nights, from 0.88 to 4.20 days after the gamma-ray event. The mean values of the degree of linear polarization (P) and its position angle (Theta) resulting from our campaign are <P>=1.18+/-0.10% and Theta = 148.7+/-2.3 deg after correcting for Galactic interstellar polarization. Our VLT data set is most naturally described by a constant degree of linear polarization and position angle, nonetheless a slow Theta evolution cannot be entirely ruled out by our data. The VLT monitoring campaign did not reveal either a significant Theta rotation respect to the Keck spectropolarimetric observations performed ~0.25 days after the GRB (Barth et al. 2003). However, <P> is a factor of two lower than the polarization degree measured from Keck. Additionally, the VLT polarization data allowed us to construct an accurate V-band light curve. The V-band photometric data revealed a smooth light curve with a break located between the last Keck and our first VLT polarimetric measurement, 0.33 < t_(break, V) < 0.88 days after the GRB. The typical magnitude fluctuations of the VLT V-band lightcurve are 0.003 mag, 0.010 mag and 0.016 mag for our three observing nights, respectively. We speculate that the stability of Theta might be related to the smoothness of the light curve.