In the absence of attributes (bow and arrow) or accompanying figures, the identification is based on similar bronzes, posture and by elimination. More about it later.
Here Rama is sitting on an inverted lotus (Padmapeetha) in a variation of lalitasana. Incidentally this cross-legged posture, ankle-on-knee, is considered rude by some in India. Strange we find that in a vigraha dating back hundreds of years.
This vigraha is an unusual combination of the vira or warrior aspect (dagger on his right hip), comfort seeking (pillow under his left thigh) and espousing wisdom (right hand’s cin mudra). This is divinity as King.
The vira aspect is emphasized by the toned body. See the rounded shoulders (deltoid muscles), the v-shaped upper back, obliques and glutes. Unusual to see such realistic portrayal.
The identification is based on other vigrahas in my collection. Rama in preaching mode shows the cin mudra and the vaishnavite religious mark on the forehead. Yoga Sitarama shows the cin mudra. The four-armed Rama has a dagger on his right hip.
The quality of casting (see the ears and the fingers on the right hand), high copper content alloy and the way the main figure is attached to the peetam (the base) suggest this Vigraha is from Tamil Nadu.
The tall crown indicates Vijayanagar influence and the vigraha may be dated to the seventeenth century or earlier. The Vigraha is about 10 cm in height.
Note: In Hindu temples circumambulation of deity is an integral part of worship. You do that by going around the deity clockwise, keeping the deity on your right. The above photos show the Vigraha as you will see it when you do circumambulations.