I tried looking to see if someone uploaded a collection of his music somewhere but surprisingly enough, I can't seem to find anything. Can someone please help?

Although Sinatra sang in a few films, his entire discography (which is huge) is not appropriate for this forum. I could be wrong, but I don't think you'll find his entire discography uploaded anywhere. There are plenty of good sites and blogs for jazz music that have lots of his albums, but I'm not going to post them because they also contain material prohibited by this blog. Maybe you could ask for a few specific soundtrack albums he sang on (assuming they're not from Varese Sarabande, etc.).