Term for the position of a man urinating into a toilet while having an erection. To make his penis point downward, a man has to spread his legs apart and lean forward, mimicking the way a giraffe spreads its front legs and leans its neck down to drink water.
"I had an erection when I woke up, so I had to do the drinking giraffe to pee."
When attempting to urinate with an erection, one must posture oneself so that the legs are splayed out wide and the torso and pelvis can roll forward, thus facilitating a downward trajectory of urine in an attempt to accurately target the toilet. Much like the Giraffa camelopardalis, or giraffe, as he gingerly prostrates himself at the local watering hole.
The extreme case of morning wood forced Jason to assume the awkward Drinking Giraffe position in order to avoid painting the ceiling with piss.