Copyright

A slogan is not registerable as a trademark. If you are only using the slogan as an ornamental design on the front of a T-shirt, you cannot register the slogan as a copyright. A trademark registration is the appropriate way to obtain protection for the slogan, but you would have to use the slogan on items other than on the front of a t-shirt to avoid a rejection by the United States Patent and Trademark Office. You have to show that you are using the slogan to identify your business as a brand identifier, so I would recommend that you use the slogan on a hang tag, on sewn-in labels and in other places. If it used only on the front of a t-shirt, it will be considered merely ornamental decoration on the front of the shirt and not a registerable trademark as a slogan. You may wish to read the provisions of the Trademark Manual of Examination Procedure at http://tess2.uspto.gov/tmdb/tmep/1200.htm#_T120203 that discusses this issue in detail.

You should also conduct a search to determine whether you have the right to use/register the slogan, in case someone else has registered it or has common law rights to it.

This is general legal advice and is not intended to create any legal relationship, I recommend seeking the advice of competent counsel for specific legal guidance.

Just to add to to the previous answer - It is kind of difficult to answer your question without knowing exactly what you had in mind for the slogan, but to generalize, the onlyway for a slogan to get protectionis if it has developed a secondary meaning. Think of " Does she or doesn't she? Only her haridresser knows for sure" (Clairol) or to be a liitle more up to date "Just Do It" (Nike). These phrases became linked to the brand so that if I youy put "Just Do It" on a t-shirt you may be infirngning on Nike's intellectual property. Similarly, if you come up with such a catchy slogan that it becomes synonymous with your brand, then you will be able to protect it, but that's a difficult thing for a start-up to do. Finally, there are State unfair competition laws that may give you some proteciton if people are unfairly competing against you with your ideas.