I don't know of any such job sites. I know recruiters exist who specialize in international placement, usually for senior executives, scientists, and academics. Unless you have rare and in-demand skills you will probably find software developers aren't that hard to find locally in most countries.
In general companies can only hire and get visas for people who have skills not available in the domestic talent pool. All kinds of exceptions and workarounds (and frauds) happen, but if you're looking for a foreign employer to jump through the hoops of relocation and obtaining a visa you will need to have some demonstrable abilities they can't hire a citizen for.
Another path is working for a company that has offices overseas. Depending on your CV that may be easy or hard. For software dev jobs you would need some advantage over local talent, who probably get paid less if you're from the USA.
Then there's freelancing. You can live wherever you want once you get some remote contracts. No relocation and no visa, that's your problem. If you need a visa, and what that involves, depends on your passport, where you go, how long you plan to stay there, and a bunch of other country-specific things.
As a US citizen I worked in the UK a long time ago, with a work visa, and that wasn't easy to get. I've freelanced remotely for over ten years now and learned to deal with visas and immigration bureaucracy. I only work for US-based companies -- they pay better and I don't have any language or cultural barriers.
