Short answer - No.
Long answer - see definition of addictive. May contain one or more of the following components - a substance which induces a euphoric or altered mental state, more and more of which is required over time to induce the same effect, for which one develops a craving, where usage is continued despite negative consequences, whose sudden discontinuance induces serious physical consequences (DT's, malaise, pain, death).
Of the above criteria, sudden discontinuance of some antidepressants is said to create unpleasant effects in some people; in most cases it is manageable through tapered reduction in dosage.
It depends on what you mean by addictive. If they work for you, then I guess you could say they're addictive, because you won't want to stop taking them because you feel better. I have found that some will give you withdrawal symptoms if suddenly stopped- I think actually most do, but some more than others. I have tried Paxil, Prozac, Effexor, and Wellbutrin. Effexor has the WORST withdrawals by far. at least out of the ones I have taken. I have not tried Lexapro because it is a bit expensive (or so my Dr told me). So I guess it depends on your definition of addictive. But, in all honesty, if it works for you, and improves your quality of life, addiction would be the last of my worries!!