We present Rossiter-McLaughlin observations of the transiting super-Earth 55 Cnc e collected during six transit events between 2012 January and 2013 November with HARPS and HARPS-N. We detect no radial velocity signal above 35 cm s^–1 (3σ) and confine the stellar v sin i to 0.2 ± 0.5 km s^–1. The star appears to be a very slow rotator, producing a very low amplitude Rossiter-McLaughlin effect. Given such a low amplitude, the Rossiter-McLaughlin effect of 55 Cnc e is undetected in our data, and any spin-orbit angle of the system remains possible. We also performed Doppler tomography and reach a similar conclusion. Our results offer a glimpse of the capacity of future instrumentation to study low amplitude Rossiter-McLaughlin effects produced by super-Earths.