"Hello, FBI? This random guy on the Internet is extorting me."

FBI: 'Go away and come back when you have a name and address, and can prove the guy is under our jurisdiction.'

Fortunately the FBI doesn't dismiss illegal activities of you lack this kind of information. They will investigate and can arrest individuals on US soil as well as consenting countries. Additionally a country's own law enforcement may cooperate and the perpetrators can be extradited for trial.

Can the FBI do anything if the culprit is not in the US?

Sort of... sometimes they will lure them to the USA or catch them while they're here if the victim has enough clout. Some here may remember when the FBI arrested Dmitry Sklyarov, for example:

https://en.wikipedia.org/wiki/United_States_v._Elcom_Ltd.

Not for an individual, they won't.

They don't work for you.