What is the bank angle that should be sustained to move in a uniform circular motion?
I hope you also appreciate help that uses the metric system. You should. It makes the calculation much simpler.

So your question is: What bank angle $\varphi$ do I get when flying a circle of a known radius $R$?

All by itself, the question cannot be answered. You need to specify a speed, either the flight speed $v$ or the angular velocity $\omega$, in order to find the proper bank angle. Then it is easy:
$$tan\varphi = \frac{v^2}{R\cdot g}\;\; \text{or}\;\;\varphi = arctan\left(\frac{v^2}{R\cdot g}\right)$$
$$tan\varphi = \frac{\omega\cdot v}{g}\;\; \text{or}\;\;\varphi = arctan\left(\frac{\omega\cdot v}{g}\right)$$
where $g$ is the gravitational acceleration and all parameters should be inserted in their SI units. $\varphi$ will be in radians!

If you don't know either speed, try some values until you get a reasonable angle, which would be not more than 30° for civilian and 75° and more for military aircraft. You can find an upper bound for that angle if you know the maximum sustained load factor of the respective plane because the roll angle and the load factor $n_z$ in a turn are directly related:
$$tan\varphi = \sqrt{n_z^2 - 1}\;\; \text{or}\;\;\varphi = arctan\left(\sqrt{n_z^2 - 1}\right)$$