By measuring femtosecond laser driven strong-field electron yields for linear molecules aligned by circularly polarized femtosecond laser pulses, we study the rotational wavepacket evolution of N-2, CO, and C2H2 gas molecules. We show that circular polarization produces a net alignment along the laser pulse propagation axis at certain phases of the evolution. This gives the possibility to control alignment of linear molecules outside the plane of polarization, which can provide new capabilities for molecular imaging. The experimental results were compared to the calculated field-free molecular alignment parameter taking into account the effects of electronic structure and symmetry of the molecules. By fitting the calculated impulsive alignment parameter to the measured experimental data we determined the molecular rotational constants of the linear gas molecules.