Different points in the earth are at slightly different distances from the sun and hence, experience different forces due to gravitation.
For a rigid body, we know that, if various forces act at various points in it, the resultant motion is as if a net force acts on the CM (centre of mass) causing translation and a net torque at the CM causing rotation around an axis through the CM. For the earth-sun system (approximating the earth as a uniform density sphere)                                             [NCERT Exemplar]

• A

  the torque is zero

• B

  the torque causes the earth to spin

• C

  the rigid body result is not applicable, since the earth is not even approximately a rigid body

• D

  the torque causes the earth to move around the sun