We are carrying out a series of photometric monitoring to measure the rotation periods of members in the young Pictoris Association, as part of the RACE-OC project (Rotation and ACtivity Evolution in Open Clusters). In this paper, we present the results for HD 155555C which is believed to be physically associated to the spectroscopic binary V824 Ara (HD 155555) and thus constituting a triple system. We collected B, V, and R-band photometric data timeseries and discovered from periodogram analysis the rotation period P = 4.43 d. Combined with stellar radius and projected rotational velocity, we find this star almost equator-on with an inclination i 90 . The rotational properties of HD 155555C fit well into the period distribution of other Pic members, giving further support to the suggested membership to the association and to its physical association to V824 Ara. A comparison with pre-main-sequence isochrones from various models allows us to estimate an age of 20 15 Myr for this triple system.