A-Best: You can't. There are no online versions of a TI-83 (Plus) calculator, at least that I know of, so it has to be downloaded.
You can download such emulators from http://www.ticalc.org/archives/files/fileinfo/84/8442.html or http://www.ticalc.org/archives/files/fileinfo/372/37211.html
Note that in order to get any of these emulators to work you'll need a ROM image file which you can obtain from a calculator you legally own. Distributing or receiving a ROM file that you do not own is illegal.