Kurt is right on the money. Short phrases cannot be copyrighted and your proposed use of someone else's trademark might be a violation depending on how you plan to use it. It appears that Twitter has obtained a federally registered trademark for the word "tweet" in connection with its online, real time communication through social networking (see the attached link). As a result, you might infringe upon Twitter's trademark if you used the term in a confusingly similar way.
On the other hand, there are permissible uses for the word "tweet" that are unrelated to the service that twitter provides. For example, if you used the word "tweet" to identify a type of bird food, consumers are unlikely to think that your product is sponsored or endorsed by Twitter as you are using the word to identify a completely unrelated product.
Furthermore, there are certain "fair use" defenses to trademark infringement, such a "classic" or "nominative" fair use defense that might apply depending on the type of use you are considering for "tweet". As Kurt correctly pointed out, it is impossible to tell at this point whether those defenses might apply with out learning more about your proposed use.
The below does not constitute legal advice, does not form an attorney-client relationship, and should not be relied upon to take or refrain from taking any action.
Single words and short phrases are ineligible for copyright protection (see Copyright Office Circular 34 on the subject, linked below). The question would be whether your use might infringe any trademark rights Twitter has in the word (if any). Unfortunately, without more information on how you plan on using the term on your posted, it is impossible to tell whether there would be an issue.
