For a circular aperture of diameter $D$, the first diffraction minimum is a circle with angular radius approximately $1.22\lambda/D$. For a square aperture of side length $a$, the first diffraction minimum (perhaps not very surprisingly) forms a square. The angular side length of this square is $2\lambda/a$.
If you are asking about the angular resolution according to the Rayleigh criterion, to resolve two nearby light sources separated along the direction of either edge of the square, the resolution limit is reached when the diffraction patterns of the two sources are $\lambda/a$ apart, so this is the diffraction limited angular resolution. You could get slightly better resolution by rotating the aperture by $45^\circ$ so that the light sources are separated along the square diagonal, in which case the resolution is $\lambda/\sqrt{2}a$.