No there is not an international trademark and if you want a registered trademark you must register in each country.
Note that in the US and some other countries you have a trademark merely by using the mark in commerce. You thus already have a trademark. What you are looking to get now is a registered trademark, which has some benefits over an unregistered (i.e. common law) trademark. See here for the benefits of registering in the U.S.
Some countries (e.g., in Europe) don't have common law trademark rights, and if you want trademark rights you must register.
If you were the first to use your mark and others are copying you in the U.S., you can send out a cease and desist letter right away. You don't need to wait until you get your registration, which might take six months.