Elon Musk’s rocket company, Space Exploration Technologies Corp., is set to raise $500 million at a $30.5 billion valuation, in a bid to help get its internet-service business off the ground, according to people familiar with the fundraising.

The Hawthorne, Calif., company, known as SpaceX, is raising the capital from existing shareholders and new investor Baillie Gifford & Co., one of the people said. The Scottish money-management firm is one of the largest investors in another Musk-led company, Tesla Inc., with about a 7.6%...