The transiting extrasolar planet XO-3b is remarkable, with a high mass and eccentric orbit. These unusual characteristics make it interesting to test whether its orbital plane is parallel to the equator of its host star, as it is observed for other transiting planets. We performed radial velocity measurements of XO-3 with the SOPHIE spectrograph at the 1.93 m telescope of Haute-Provence Observatory during a planetary transit and at other orbital phases. This allowed us to observe the Rossiter-McLaughlin effect and, together with a new analysis of the transit light curve, to refine the parameters of the planet. The unusual shape of the radial velocity anomaly during the transit provides a hint of a nearly transverse Rossiter-McLaughlin effect. The sky-projected angle between the planetary orbital axis and the stellar rotation axis should be λ = 70° ± 15° to be compatible with our observations. This suggests that some close-in planets might result from gravitational interaction between planets and/or stars rather than migration due to interaction with the accretion disk. This surprising result requires confirmation by additional observations, especially at lower airmass, to fully exclude the possibility that the signal is due to systematic effects. Based on observations collected with the SOPHIE spectrograph on the 1.93 m telescope at Observatoire de Haute-Provence (CNRS), France, by the SOPHIE Consortium (program 07A.PNP.CONS).