Answer
Yes, this is possible.
Work Step by Step
If the axis of rotation is parallel to the external magnetic field, there will be no flux through the loop at any time. With no change in flux, there will be no induced emf.
For example, if the magnetic field were oriented vertically, the square loop should be in a vertical plane, with 2 sides horizontal and the other 2 sides vertical.
There is no flux through the loop, and as the loop rotates about one of the vertical sides, there will still be no flux, and hence no emf.