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We investigate the DC Josephson effect in a superconductor-normalmetal-superconductor junction where the normal region consists of a ballisticring. We show that a fully controllable $\pi$-junction can be realized throughthe electro-magnetostatic Aharonov-Bohm effect in the ring. The sign and themagnitude of the supercurrent can be tuned by varying the magnetic flux and thegate voltage applied to one arm, around suitable values. The implementation ina realistic set-up is discussed.Comment: 4 pages, 3 figure

Switching the sign of Josephson current through Aharonov-Bohm interferometry