I do, and I just post a preview--actually well that's not quite right: I post a cropped version of the art, then also a full version of the art with no captions (it's widescreen, so the full art doesn't necessarily come through that easily on small screens in Instagram). The link to my webcomic is in my bio (you only get one clickable link there, make it count! : D), and recently I've started making explicit mention of that when I post a preview image (like "This is art from the latest page of my webcomic (link in bio)").
I noticed my page hits go up from about 3 K per day to about double that once I started posting on Instagram, so either it's a phenomenal coincidence, or it works rather well for me. Plus, it's free, so you're not losing much except a few minutes of your life making a post, I guess. ^_^
I think maybe (?) click-throughs from Instagram might be hard for trackers to spot, because the clicks come from an app rather than another web page--so they don't have the usual HTTP REFERER URL in their header that gets logged by your web server and read by analytic software to tell you where they came from. Or at least, such is my theory--I don't actually know!