May I still obtain AppleCare if I purchase a phone from AT&T?

Yes. The easiest way is to buy it directly from AT&T at the same time as you buy your phone. They may try to sell you their own protection or insurance plan so be sure to fully understand what it is that you are buying. See: https://www.att.com/support/article/wireless/KM1045162

You can also buy AppleCare directly from Apple later but you need to do it within 60 days and it may require inspection or remote diagnostics to proceed with the purchase. See: AppleCare Products - iPhone - Apple