There's three possibilities here 
You're not actually adding the path to your $PATH
 
You're adding the path to your $PATH but the laravel CLI isn't installed 
 
You're adding the wrong path to your $PATH
 
All of which every new unix shell users has stumbled with before, so don't feel bad!
First, I'd make sure the laravel CLI is installed by trying to run it with the following
$ ~/.composer/vendor/bin/laravel
Assuming the above doesn't result in an error message, it means the command is installed.
Assuming you have the command installed, this means whatever you're doing to add the path to your $PATH isn't working.  Try echoing out the path in your shell
$ echo $PATH
I bet you don't see ~/.composer/vendor/bin/laravel in there.  If that's the case, update your question with information on what you're doing when you "set the path to the ~/.composer/vendor/bin" or "add the path to the ~/.bashrc file,".  Chances are you're doing something wrong there. 
Also, if you could include the output from echo $PATH that'd be useful for people who want to help you track this down.