I assume that the angle is opposite the side a.

If so:

1. Draw the side a which has the endpoints B and C.

2. Draw the perpendicular bisector of a.

3. Draw in B (or C) the angle with a as one leg.

4. The other leg of the angle cuts the perpendicular bisector in M, the midpoint of the circumscribed circle.

5. Have a look here: Central Angle Theorem - Math Open Reference