It's not easy to figure out, but if you have a Southwest Rapid Rewards Visa it's possible through More Rewards.
Here's a previous discussion. I posted a detailed explanation on page 2.
Log in to the Southwest website, and under Rapid Rewards, click on More Rewards. Near the upper right hand corner, under Travel click on Rental Cars. That will load a page with many rental car company gift card options, but the very first link should be Book Travel Now. Select that, then choose Car from the top menu.
