  The Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) effect plays an important
role in the rotational properties and evolution of asteroids. While the YORP
effect induced by the macroscopic shape of the asteroid and by the presence of
surface boulders has been well studied, no investigation has been performed yet
regarding how craters with given properties influence this effect.
  We introduce and estimate the crater-induced YORP effect (CYORP), which
arises from the concave structure of the crater, to investigate the magnitude
of the resulting torques as a function of varying properties of the crater and
the asteroid by a semi-analytical method.
  The CYORP torque can be comparable to the normal YORP torque when the size of
the crater is about one-tenth of the size of the asteroid, or equivalently when
the crater/roughness covers one-tenth of the asteroid's surface. Although the
torque decreases with the crater size, the combined contribution of all small
craters can become non-negligible due to their large number when the commonly
used power-law crater size distribution is considered. The CYORP torque of
small concave structures, usually considered as surface roughness, is essential
to the accurate calculation of the complete YORP torque. Under the CYORP effect
that is produced by collisions, asteroids go through a random walk in spin rate
and obliquity, with a YORP reset timescale typically of 0.4 Myr. This has
strong implications for the rotational evolution and orbital evolution of
asteroids.
  Craters and roughness on asteroid surfaces can influence the YORP torques and
therefore the rotational properties and evolution of asteroids. We suggest that
the CYORP effect should be considered in the future investigation of the YORP
effect on asteroids.
