Context : We present new high-resolution spectroscopic observations for 91 pre-main sequence stars in the Orion Nebular Cluster ( ONC ) with masses in the range 0.10 - 0.25 M _ { \odot } carried out with the multi-fiber spectrograph flames attached to the UT2 at the Paranal Observatory . Aims : Our aim is to better understand the disk-locking scenario in very low-mass stars . Methods : We have derived radial velocities , projected rotational velocities , and full width at 10 % of the H \alpha emission peak . Using published measurements of infrared excess ( \Delta ( I _ { C } - K ) ) , as disk tracer and equivalent width of the nead-infrared Ca ii line \lambda 8542 , mid-infrared difference [ 3.6 ] - [ 8.0 ] \mu m derived by Spitzer data , and 10 % H \alpha width as diagnostic of the level of accretion , we have looked for any correlation between projected angular rotational velocity divided by the radius ( v \sin i / R ) and presence of disk and accretion . Results : For 4 low-mass stars , the cross-correlation function is clearly double-lined indicating that the stars are SB2 systems . The distribution of rotation periods derived from our v \sin i measurements is unimodal with a peak of few days , in agreement with previous results for M < 0.25 M _ { \odot } . The photometric periods were combined with our v \sin i to derive the equatorial velocity and the distribution of rotational axes . Our < \sin i > is lower than the one expected for a random distribution , as previously found . We find no evidence for a population of fast rotators close to the break-up velocity . A clear correlation between v \sin i / R and \Delta ( I _ { C } - K ) has been found . While for stars with no circumstellar disk ( \Delta ( I _ { C } - K ) < 0.3 ) a spread in the rotation rates is seen , stars with a circumstellar disk ( \Delta ( I _ { C } - K ) > 0.3 ) show an abrupt drop in their rotation rates by a factor of \sim 5 . On the other hand , only a partial correlation between v \sin i and accretion is observed when other indicators are used . The X-ray coronal activity level ( \log L _ { X } / L _ { bol } ) shows no dependence on v \sin i / R suggesting that all stars are in a saturated regime limit . The critical velocity is probably below our v \sin i detection limit of 9 km s ^ { -1 } . Conclusions : The ONC low-mass stars in our sample , close to the hydrogen burning limit , at present seem to be not locked , but the clear correlation we find between rotation and infrared color excess suggests that they were locked once . In addition , the percentage of accretors seems to scale inversely to the stellar mass .