In theory, I think you could, but I wouldn't recommend trying.
As far as I can determine, the TSA has taken no public position on the permissibility of leeches, and that is all that can be said definitively. But since this is an invitation to speculation, allow me to speculate.
The official list of prohibited items are mainly things that can be used as weapons, as well as liquids or gels of any kind in containers larger than 100mL. Food is not excluded from the liquid restriction, so don't claim that they are for live bait or bird feed— or for your famous river bottom stew— as that will get you nowhere.
In theory you could declare them as medicinal, as there are legitimate modern medical uses for leeches, but the uses are very limited (e.g. post-surgery) and I doubt you could find a medical professional who would write you a letter saying you must bring them on board. You could probably carry them in your checked luggage. And leeches are found on every inhabited continent, and probably not overly difficult to obtain at your destination.
The most promising option, then, would be to declare them as pets. Leeches are a legitimate addition to an aquarium, and pets are exempt from the liquid restriction provided you can demonstrate that they are alive. For example, live fish are allowed if they are in a clear spill-proof containers so that the screener can see them swimming around, thus demonstrating that the water does not contain a high concentration of explosives or toxins. This might be harder to demonstrate with leeches; pick ones that are extra-wriggly.
But airport screeners can still, at their discretion, exclude or require additional screening of other items which in their judgment could endanger passengers. Given the visceral reaction most people have even to the word leech, and given that it is in fact a bloodsucking worm which secretes a substance that promotes bleeding, it would not be unexpected for them to disallow them— consider that past "threatening" items have infamously included applesauce, guppies, medical urostomy bags, and an 82-year-old breast cancer survivor's prosthetic breast. (But not to soapbox).
Incidentally, even if you do get your leeches through the TSA checkpoint, you still might not be allowed to take them on board an airplane. Airlines have their own policies on items permitted in the cabin; for example, there is no TSA restriction on durian, but if a gate agent for Singapore Airlines sees (or smells) you with it in the SFO departure lounge, you won't be let through the gate. Similarly, airlines are generally okay with cats or rabbits in pet carriers, but generally not hamsters or snakes. How the cabin crew might react to your jar of leeches is anyone's guess.