Answer
$V = -\frac{q}{\pi~\epsilon_0}$
Work Step by Step
We can write a general equation for the electric potential:
$V = \frac{1}{4\pi~\epsilon_0}\sum \frac{q_i}{r_i}$
Note that the electric potential from each charge cancels out with an equal and opposite charge, except for the $-2q$ charges at the top and bottom of the square.
We can find an expression for the net electric potential:
$V = \frac{1}{4\pi~\epsilon_0}(\frac{-2q}{d}+\frac{-2q}{d})$
$V = -\frac{4q}{4\pi~\epsilon_0}$
$V = -\frac{q}{\pi~\epsilon_0}$
