If you're talking about inactive ingredients (like the gelatine or other binding ingredients) that are vegan-friendly, then yes, there are options. I had a look through the drug fact sheets online for a few popular anti-depressants. These are the non-generic brands, so they'll be a few dollars extra than a generic. Generic brands have the same active ingredients, but not necessarily the same inactive ingredients (which is where you stumble across non-vegan stuff like gelatine)
As far as I could tell, although you should probably double-check with your doctor (he/she will have access to drug information sheets too, which will list their inactive ingredients)
CIPRAMIL tablets (citalopram) CONTAINED inactive animal ingredients.
ZOLOFT (sertraline) tablets contained no inactive animal ingredients.
LEXAPRO (escitalopram) film-coated tablets contained no inactive animal ingredients. The film coating is hypromellose, a vegetarian alternative to gelatine.
EFFEXOR XR (venlafaxine) CONTAINED inactive animal ingredients.
AROPAX (paroxetine) ???? There's an ingredient called 'polysorbate 80' that could be animal-based. Not sure. Ahhhh just realised you're from America, you have PAXIL over there, which is the equivalent of AROPAX. PAXIL isn't vegan as far as the non-active ingredients go.
As non-active ingredients can vary a lot between name brands and generic brands, you might have a shot at finding a generic version of what you're taking now. Do you mind if I ask what it is you're currently taking? I can have a look and see if any generics come up and I'll read through their ingredients.