Most major planetary bodies in the Solar System rotate in the same direction as their orbital motion: their spin is prograde. Theoretical studies to explain the direction as well as the magnitude of the spin vector have had mixed success. When the accreting building blocks are ∼ km-size planetesimals - as predicted by the classical model - the accretion process is so symmetric that it cancels out prograde with retrograde spin contributions, rendering the net spin minute. For this reason, the currently-favored model for the origin of planetary rotation is the giant impact model, in which a single collision suffices to deliver a spin, which magnitude is close to the breakup rotation rate. However, the giant impact model does not naturally explain the preference for prograde spin. Similarly, an increasing number of spin vector measurement of asteroids also shows that the spin vector of large (primordial) asteroids is not isotropic. Here, we re-assess the viability of smaller particles to bestow planetary bodies with a net spin, focusing on the pebble accretion model in which gas drag and gravity join forces to accrete small particles at a large cross section. Similar to the classical calculation for planetesimals, we integrate the pebble equation of motion and measure the angular momentum transfer at impact. We consider a variety of disk conditions and pebble properties and conduct our calculations in the limits of 2D (planar) and 3D (homogeneous) pebble distributions. We find that in certain regions of the parameter space, the angular momentum transfer is significant, much larger than with planetesimals and on par with or exceeding the current spin of planetary bodies. We link this large net spin delivery to the appearance of asymmetries during the accretion process of pebbles. For example, prograde contribution may dominate (in certain regions of the parameter space) because they originate from trajectories that are preferentially captured. For simplicity, our calculations have ignored certain important effects (e.g., collisions, the back-reaction on the gas, and formation of atmospheres) and do not address how the eventual distribution of spin vectors is obtained for which collisions and post-formation processes must have played a role to explain the scatter. Irrespective of these issues, pebble accretion is a viable mechanism to not only grow planetary bodies, but also to impart them with a significant spin.