If your 650 Watt PSU has a maximum combined +12 Volt continuous current rating of 38 Amps or greater and has at least one 6-pin and one 8-pin PCI Express supplementary power connectors then it should be sufficient.
E.g. Seasonic M12II Bronze Series 650W (SS-650AM Active PFC F3)
• maximum combined +12 Volt continuous current rating of 53 Amps
• four (6+2)-pin PCI Express supplementary power connectors
That M12II-650 Bronze would be way more than sufficient to power a system with a single Radeon R9 280X.