You can through the Dropbox app. Upper right corner, hit the button that shows three dots. Click on Add Files and go from there.
Edit: if I've read the post right, that is. LOL This is to upload from phone to Dropbox.
Regarding posting a Dropbox link here, oddly enough, I can't get it to paste a link in the mobile version of this site using Safari on the phone, though it pastes fine in other apps. But since stridemat says it works, I'm betting that's an issue on my end.