Your avatar should automatically switch his rifle to his left shoulder when stepped out to the left (using Ctrl+A). This would allow you to effectively engage to the left side of cover without having to expose your entire body.
This should only happen with weapons that can be safely fired in such way though, i.e. not bullpup weapons that would eject empty casings and/or hot gasses directly into your face. {F18544} {F18545}