There is a surprisingly large number of moths in the family Geometridae whose caterpillars “look like a stick”. Beyond that very general description, the caterpillars have huge variation: little pinstripes, big, bold black markings, warts and bumps and protuberances, and generally it is very difficult to pin down just which Geometrid moth caterpillar, or inchworm, you have.
I am 99% sure this is the caterpillar of the oak beauty moth, Phaeoura quernaria, or Hodge #6763.
Geometrid moth caterpillars are known as inchworms — they all have the same gap between the front and back legs and move with an inching, or looping gait, reaching out with their front end, grasping, and then pulling their back end behind them. Many (though not all) of them are extremely cryptically camouflaged, and very difficult to find when on the right foliage! Sometimes they will even freeze with their front ends held stiffly in the air, greatly resembling a broken-off twig.