C++ code? No. Without a C++ compiler, you can not run C++ code.
There are a few interpreted languages that you can use on most computers, such as Jscript, and if you are truly a glutton for punishment, it is possible to directly enter a DOS executable in machine instructions that will run if the OS still supports a virtualized DOS machine.
However, check your school policy on what you are permitted to use on their machines. Many people tend to freak out when they see a student doing anything with a command prompt.
If the school allows you internet access you can use ideone.com if all you need is to test the code. If you want to run the executable locally, then no there isn't.