In addition to the bow and arrow, he is also carrying a dagger. See the right view. Yes, I have a classical bronze of Rama with a dagger.
The features worth noting include belt holding the lower garment and the dagger, tassels in the lower garment, Jatamukuta rather than a crown and long earlobes. His moustache deserves a separate mention.
The Kosuvam (small fold of the lower garment) at the back suggests this bronze may be from South India.
Quality of casting (ears and patterns on the garment) and the details (neckwear, full bow) suggest this was made for worship. There are obvious signs of worship relater wear. The patination is deep.
This bronze is solid cast. This is about 14 cm in height. This may date to the eighteenth century.
13 Dec 2018: B N Aryan opined this is from Tamil Nadu and dates to the nineteenth century.
5 Jan 2019: Reproducing comments received from Krishna, one of my go-to persons.
“This bronze is, in my humble opinion, is Kirathamurthy – a form of Lord Shiva as a hunter. The reason for my identifying this piece as such are three features: 1) mustache (usually Rama is shown in paintings as having a mustache, or beard, but not in bronzes), 2) dagger at the waist, and 3) the arrow held is with the tip pointed downwards (usually Rama’s arrow is pointed upwards). Additionally, the longbow style bow held is also the type shown in Kirathamurthy’s left hand.
Attached are a few references for Kirathamurthy so you can review, and make a determination. Most commonly, his right hand rests on the handle of the dagger, tucked at the waist. More rarely, he holds the arrow, with the tip pointed downwards. The silve statue is the utsava murthy of Ayyappa in Sabarimala (here Ayyappa is identified with Sastha, of which Kirathamurthy/Kiratha Sastha is one of the celebrated forms). This may seem somewhat fluid, but Sastha worship in Kerala is very much so (much reading has brought me to this conclusion!).