Upvote:2
Assuming you're from a VWP country, you're still eligible to apply for an ESTA: being previously refused a visa doesn't make you inadmissible.
That said, you will be asked on the application form about whether you've ever been refused a visa, and it's highly likely that the ESTA will be denied:
If you were previously denied a visa, or previously refused entry to the United States, or previously removed from the U.S., your ESTA application will most likely be denied.
If an ESTA is refused they refund $10 of the $14 application fee, so it doesn't hurt to try for $4, but I imagine it's unlikely to be approved.