Yes, "exotic" frequently has a racist connotation. The primary reason for this is because of statements like this:
Have you seen the new girl? She is so exotic!
If her exoticness is related to her race, then you are making a big deal out of her race which is, almost by definition, racist.
This doesn't mean that all uses of "exotic" are inherently racist but it is definitely a word that should be used with care. If you are at all concerned with it sounding racist you should find an alternative.
An example of a non-racist example:
I just bought some exotic fish for my aquarium!
We have planned a trip to exotic Egypt!
The racist connotations mostly apply when using the word to describe a person.
Alright, since people seem to be completely misunderstanding this issue I'll clarify a few things. The primary reason "exotic" can be problematic is because the only way you can immediately label someone "exotic" is by their appearance. In the United States, minority ethnic groups can extremely sensitive about being singled out due to their race.
If you refer to someone as "exotic" because they appear Indian, it is very likely to turn the conversation awkward. Especially if they grew up two blocks away from you and are for all intents and purposes American.
Furthermore, the connotation of "exotic" is one of labelling someone as belonging to a different culture or group. Calling someone exotic essentially puts them on a pedestal and casually implies they do not belong to your own culture. Doing this based simply on appearances is racist and potentially offensive.
If someone actually is from a "exotic" culture it is much more acceptable to describe them as exotic. The issue is jumping the gun and committing a faux pas by assuming anyone who looks foreign must be exotic.
For what it is worth, this may be a "bigger" issue in the United States where racial tensions tend to be rather awkward. White people have gained a reputation for being racially exclusive. Automatically clumping entire ethic groups into a label of "exotic" isn't considered polite. It's an age old cultural sore spot.