What kind of plug adapter do I need?
It's very likely to be a proprietary connector. Even if it conforms to a standard size like DIN (as @Trout suggests), that doesn't really tell you anything about the electrical requirements. The part your missing may have a transformer, a dimmer, or allowed ganging of several lights together.

Unless you find more markings on the bulb or cable, I would not assume anything about the lamp — could be DC or AC, could be 220V, 110V, or low voltage.

(You don't say what country you live in or whether the lamp is likely to be foreign. There are several countries that use plugs with 3 round pins in approximately the configuration of your plug, but yours looks smaller. It's a little hard to tell scale from that photo... any chance of pin-to pin-measurements?)