Yes! You can log in to Schoolrunner from any computer that's connected to the internet, whether you're at home, school, or somewhere else. You just need to know the correct login address for your school. It will look something like YOURSCHOOL.schoolrunner.org. You'll just have to replace "YOURSCHOOL" with the correct name (domain) for your school.
You may have gotten a document with your username and password that looks like this, and which lists your login address:
If you have any questions, ask your teacher for the correct address.