Yes. The Supreme Court is capitalized because it is a proper noun referring to a governmental judicial body that oversees the law of the land. This includes the highest court in each state, such as the California Supreme Court. However, when referring to generic supreme courts, such as in this sentence, you do not need to capitalize it.
What about capitalizing the word court?
According to lawprose.org, the word “court” should not be capitalized unless included in the title of a specific court, such as the “Supreme Court.”
For more answers to capitalization questions, see our FAQs or try out our free capitalization tool.