For those on Windows 10 Anniversary Edition who want a slightly more convoluted (but somewhat built-in) way to run curl you can use bash on Windows:
Turn on ‘Developer Mode’ in settings: Settings > Update and Security > For Developers
Then add the feature ‘Windows Subsystem for Linux’: Right click start > Programs and Features > Turn Windows Features On and off
Open up a command window and type bash
After it installs you’ll have curl (and more fun unix-y stuff)