Looking at the source code, the tsc command invokes a JS script tsc.js, which has 2 backends: Node.js and Windows Scripting Host. If any other JavaScript server supports reading and writing to a file system (like Rhino with RingoJS), it should be able to run the TypeScript compiler tsc.js.
Moreover, there is a fork of TypeScript compiler which claims to directly run on Rhino. So you could invoke Rhino directly from Java, without installing node.js.