Aims. The rotation state of small asteroids is affected by the Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) torque. The directly observable consequence of the YORP effect is the secular change of the asteroid's rotation period. We carried out new photometric observations of asteroid (1620) Geographos in 2008 to extend the time line that, if long enough, would enable us to see possible deviations from a constant period rotation. Methods. We used the lightcurve inversion method to model the shape and spin state of Geographos. We assumed that the rotation rate evolves in time as $omega(t) = omega_0 + upsilon t$, where both the constant term of the rotation rate $omega_0$ and the linear term υ are parameters to be optimized. In total, we used 94 lightcurves observed in 1969-2008. Results. We show that for $upsilon = 0$, a constant-period model, the whole dataset of lightcurves cannot be satisfactorily fitted. However, when relaxing υ in the optimization process we obtain an excellent agreement between the model and observations. The best-fit value $upsilon = (1.15 \pm 0.15)$ $\times$$10^{-8}~{\rm rad~d}^{-2}$ implies that Geographos' rotation rate accelerates by $\simeq$2.7 ms yr -1. This is in agreement with the theoretically predicted value 1.4 $\times$$10^{-8}~{\rm rad~d}^{-2}$ obtained from numerical integration of YORP torques acting on our convex shape model. Geographos is only the third asteroid (after (1862) Apollo and (54509) YORP) for which the YORP effect has been detected. It is also the largest object for which effects of thermal torques were revealed.
