We study the effect of rotation during the collision between dust aggregates, in order to address a mismatch between previous model calculations of Brownian motion driven aggregation and experiments. We show that rotation during the collision does influence the shape and internal structure of the aggregates formed. The effect is limited in the ballistic regime when aggregates can be considered to move on straight lines during a collision. However, if the stopping length of an aggregate becomes smaller than its physical size, extremely elongated aggregates can be produced. We show that this effect may have played a role in the inner regions of the solar nebula where densities were high.