Edit: Reply below was based on original post specifying X^TX \succeq I and is no longer applicable .
The constraint is going in the wrong direction to be convex. It is a non-convex BMI.
If you were willing to constrain X to be square symmetric positive definite, you could use [X eye(n);eye(n) X] == semidefinite(2*n)
But this is not the problem you specified, so I am marking this non-convex.
Edit: Note that more parsimoniously, you could instead use norm(x) <= 1, which is also equivalent to X^TX \preceq I and I think would get boiled down inside CVX to more or less the same thing as the above Schur complement formulation.