I kegged an IPA last Sunday (09/17) and the beer has been under 12 PSI since at approximately 40F. The beer is very under carbonated at this point.
Is there a chart, or some other means, to determine how long it will take to carbonate at a certain PSI?
Using head pressure only, it will take weeks, especially in a corny where the surface-to-volume ratio is low. Lying the keg on its side and/or agitating it will help.
Leaving them alone like that has always taken about 2 weeks in my experience.
As said, shaking/rolling it around a little, and/or laying it down on its side will make it go faster.
HTH-
Yep. It’s temp/pressure related. For most beers, target your carbonation in the green band (~ 2.5 volumes for average beers, maybe 2 for bitters, 3+ for Belgians). It takes 2 weeks to get fully carbed with this method.
You can run the chart as is, or carb faster like many do. Set your regulator to 30 psi for 2 days, then drop to 12 psi for the third day. After that, set to serving psi (around 8-10 for me), pull pressure relief, and drink away!
Definitely not as accurate as the chart and 2 wks though. But I don’t like to wait. 
That’s how I do it, too, though I leave it at 12 psi after 30psi/2 days (long serving lines). Just wanted to post the chart for him.