Laser induced Ionization We know that when a linearly polarised laser field interacts with a diatomic molecule ionization happens when the molecular axis is along the laser-field direction. 
However, in case of a circularly polarised light, it is seen that ionization can happen when laser electric field is perpendicular to the molecular axis as well (ionization along the laser-field direction is still dominant).
How can we understand this mechanism?
 A: Maybe it is too late to answer this question but let me give you an answer for you and for those who see this question. Around the intensity of the laser field of $10^{15}$
$W/cm^2$, both a tunneling ionization and a over-the-barrier ionization can take place depending on the type of molecule or timing of a pulsed laser field. With low ionization energy and at the time when the pulsed laser field peaks, over-the-barrier ionization can take place. Otherwise, tunneling ionization takes place.
About the first sentence of your question; yeah a diatomic molecule can be ionized by a linearly polarized strong laser field, but not only when the molecule is aligned with the laser field. A diatomic molecule can be ionized when it is aligned perpendicular to the linearly polarized laser field. The ionization rate can be different and in almost all cases you can expect higher ionization rate for the case when the molecule is aligned parallel to the linearly polarized laser field. Thus the same argument can be applied even when you use a circularly polarized laser field, all you have to do is to rotate the polarization angle (or the molecule) over time, during the laser field oscillation.
