We present time-resolved optical spectroscopy of the counterpart to the high-inclination black hole low-mass X-ray binary Swift J1357.2-0933 in quiescence .
Absorption features from the mass donor star were not detected .
Instead the spectra display prominent broad double-peaked H \alpha emission and weaker He i emission lines .
From the H \alpha peak-to-peak separation we constrain the radial velocity semi-amplitude of the donor star to { K _ { 2 } } > 789 km s ^ { -1 } .
Further analysis through radial velocity and equivalent width measurements indicates that the H \alpha line is free of variability due to S-wave components or disc eclipses .
From our data and previous observations during outburst , we conclude that long-term radial velocity changes ascribed to a precessing disc were of low amplitude or not present .
This implies that the centroid position of the line should closely represent the systemic radial velocity , \gamma .
Using the derived \gamma = -150 km s ^ { -1 } and the best available limits on the source distance , we infer that the black hole is moving towards the Plane in its current Galactic orbit unless the proper motion is substantial .
Finally , the depth of the central absorption in the double peaked profiles adds support for Swift J1357.2-0933 as a high-inclination system .
On the other hand , we argue that the low hydrogen column density inferred from X-ray fitting suggests that the system is not seen edge-on .