Context : There is evidence in the 125-Myr Pleiades cluster , and more recently in the 5-Myr NGC 2264 cluster , that rotation plays a key role in the Lithium ( Li ) depletion processes among low-mass stars .
Fast rotators appear to be less Li-depleted than equal-mass slow rotators .

Aims : We intend to explore the existence of a Li depletion - rotation connection among the \beta Pictoris members at an age of about 24 Myr , and to use such correlation either to confirm or to improve the age estimate based on the Lithium Depletion Boundary ( LDB ) modeling .

Methods : We have photometrically monitored all the known members of the \beta Pictoris association with at least one Lithium equivalent width ( Li EW ) measurement from the literature .

Results : We measured the rotation periods of 30 members for the first time and retrieved from the literature the rotation periods for other 36 members , building a catalogue of 66 members with measured rotation period and Li EW .

Conclusions : We find that in the 0.3 < M < 0.8 M _ { \odot } range , there is a strong correlation between rotation and Li EW .
For higher mass stars , no significant correlation is found .
For very low mass stars in the Li depletion onset , at about 0.1 M _ { \odot } , data are too few to infer a significant correlation .
The observed Li EWs are compared with those predicted by the Dartmouth stellar evolutionary models that incorporate the effects of magnetic fields .
After decorrelating the Li EW from the rotation period , we find that the hot side of the LDB is fitted well by Li EW values corresponding to an age of 25 \pm 3 Myr in good agreement with independent estimates from the literature .