So Senator Lindsey Graham thinks is in violation of the law of armed conflict (LOAC):
The overall problem with this claim is that Tsarnaev is not a belligerent in any armed conflict. To be a belligerent in terms of the (LOAC), one need to be involved in an armed conflict. There are only two types of armed conflict recognized by the LOAC: international and non-international. As far as I am aware we are not at war with Russia (of which Chechnya is a federal subject) so Tsarnaev is not a belligerent in an international armed conflict. Nor is there a civil war going on in the US.
Maybe, just maybe, if he can be tied to insurgent groups in Afghanistan or Iraq. And again, maybe, just maybe, if we think there are still civil wars going on in those countries then maybe he is a belligerent.
But from all the information there is a present, it appears Tsarnaev is a terrorist plain and simple. And should be dealt with as such. The US has ample legal resources at its call to do this without the need of expanding the definition of “belligerent” beyond its meaning.