Molecular photoelectron angular distributions (MPADs) by intense (I0 ≥ 10(14) W/cm(2)) circularly polarized ultrashort, few cycle (attosecond) ultraviolet laser pulses are presented from numerical solutions of time dependent Schrödinger equations. For the aligned molecular ion H2(+), the MPADs exhibit rotations with respect to the polarization and molecular symmetry axes which are determined by the symmetry of the initial electronics states. It is also found that the rotation angle of MPADs is insensitive to the pulse intensity. We attribute these effects to the asymmetry between the parallel and perpendicular (to the molecular axis) polarization photoionization. Influence of the molecular alignment and ionizing pulse ellipticity on the rotation of MPADs is also shown to allow control of the nonsymmetric ionization.