In a way there is nothing illegal about offering links to another site. But subtitles are a derivative work of the original text so they are copyrighted and also you typically only need subtitles for movies obtained in a questionable way. So you immediately get involved in legally shady stuff.
The main problem is that if you get sued you stand to lose a lot of money, even if you eventually win.
Reason why I'm asking is because I don't know, and obviously I don't feel like getting in trouble for a weekend hobby project.