Bilayer graphene quantum dots with rotational stacking faults (RSFs) having different rotational angles were studied. Using the first-principles calculation, we determined that these stacking faults could quantitatively modulate the magnetism and the distribution of spin and energy levels in the electronic structures of the dots. In addition, by examining the spatial distribution of unpaired spins and Bader charge analysis, we found that the main source of magnetic moment originated from the edge atoms of the quantum dots. Our research results can potentially provide a new path for producing all-carbon nanodevices with different electrical and magnetic properties.