A population of small main-belt asteroids residing on closely similar orbits was revealed by Vokrouhlicky and Nesvorny (2008, Astron. J. 136, 280-290). We have estimated statistical significances of individual pairs (Pravec and Vokrouhlicky 2009, Icarus, in press) and started a photometry observing program to characterize their spin properties. Observations of 20 primaries (larger members of asteroid pairs) reveal that primaries of pairs with small secondaries rotate rapidly, while primaries of pairs with large secondaries show significantly slower rotations. Specifically, eight observed primaries of pairs with the secondary-to-primary size ratio D2/D1 < 0.4 (estimated from the difference between absolute magnitudes of pair members Delta H > 2.0) show primary rotation periods from 2.5 to 4.4 h, while primaries of pairs with D2/D1 between 0.4 and 0.7 show slower rotations with median period of 7.2 h. The observed distribution of primary spin rates is consistent with a proposed formation mechanism of asteroid pairs by a rotational fission of the parent body or a gentle split of a binary pair. The correlation between the primary spin and the secondary-to-primary size ratio suggests that a part of the primary rotational angular momentum is transferred to the relative motion of the system's components during separation. For smaller secondaries, an insignificant fraction of the primary's angular momentum is needed to split the pair; above the largest size ratio ( 0.7) there is insufficient spin energy to effect an escape of a pair and it must remain bound. This work was supported by the Grant Agency of the Czech Republic, Grant 205/09/1107.