How long will it take for me to recover from a CT angiogram procedure?

Minutes. Unless you have an allergic reaction to the IV contrast, the warm feeling from the contrast is over in minutes. You will have a band-aid from the iv, but will otherwise feel normal.
Very little. Ct angiogram is a ct where the images are taken during contrat injection through an IV in the arm. There is no recovery period other than IV removal and bandage placement. Draining fluids helps eliminate the contrast.