ABSTRACT Ly α emission lines are typically found to be redshifted with respect to the systemic redshifts of galaxies, likely due to resonant scattering of Ly α photons. Here, we measure the average velocity offset for a sample of 96 z ≈ 3.3 Ly α emitters (LAEs) with a median Ly α flux (luminosity) of ${≈}10^{-17}~\rm erg~cm^{-2}~s^{-1}$ (${≈}10^{42}~\rm erg~s^{-1}$) and a median star formation rate (SFR) of ≈1.3 $\rm M_{⊙ }~yr^{-1}$ (not corrected for possible dust extinction), detected by the Multi-Unit Spectroscopic Explorer as part of our MUSEQuBES circumgalactic medium (CGM) survey. By postulating that the stacked CGM absorption profiles of these LAEs, probed by eight background quasars, must be centred on the systemic redshift, we measure an average velocity offset, Voffset = 171± 8 km s−1, between the Ly α emission peak and the systemic redshift. The observed Voffset is lower by factors of ≈1.4 and ≈2.6 compared to the velocity offsets measured for narrow-band-selected LAEs and Lyman break galaxies, respectively, which probe galaxies with higher masses and SFRs. Consistent with earlier studies based on direct measurements for individual objects, we find that the Voffset is correlated with the full width at half-maximum of the red peak of the Ly α line, and anticorrelated with the rest-frame equivalent width. Moreover, we find that Voffset is correlated with SFR with a sub-linear scaling relation, $V_{\rm offset}∝ \rm SFR^{0.16± 0.03}$. Adopting the mass scaling for main-sequence galaxies, such a relation suggests that Voffset scales with the circular velocity of the dark matter haloes hosting the LAEs.