Goldman Sachs has led an $81 million investment in online consignment store ThredUp Inc., a move that marks the financial firm’s growing appetite for startups and a record investment in one of nearly a dozen such companies building online thrift shops.

From streaming music service Spotify to database management platform MongoDB, Goldman Sachs has made more than two dozen investments in privately held tech companies so far this year, according to Dow Jones VentureSource.

Goldman...