The exploding popularity of animated GIFs online is attracting serious interest from venture investors.

Giphy Inc., a search engine for the short, looping video files that are all the rage on social media, has raised a fresh $72 million round of equity funding from lead investor Draper Fisher Jurvetson, as well as Institutional Venture Partners and China Media Capital. These new investors join previous backers Betaworks, RRE Ventures, Lightspeed Venture Partners and Alphabet Inc.’s GV.

The...