You can do this, yes, but the two domains will need to have trust between each other, so that you can authenticate still.
Access the SSRS portal, and hover over the folder you want to give users access to and click security (See screenshot 1).
The folder is probably set to inherit permissions, so click Edit Item Security, Which should provide you with a pop up asking if you're sure you want to apply different security settings to the parents, Click ok. Now click "New Role Assignment". Enter the name/group (with Domain) that you want to have access to the folder, and the role they need (see Screenshot 2) and click ok.
The users will then be able to access reports in that repository.
Excuse my typos and sometimes awful grammar. My fingers work faster than my brain does.