A verb meaning to have something pointed "inserted" on one's leg?

If you're specifically talking about a bird, the word you're looking for might be "peck".

"The bird pecked my arm with its beak."

jab [jab]

verb (used with object), verb (used without object), jabbed, jab·bing.

1. to poke, or thrust abruptly or sharply, as with the end or point of a stick.

"The bird jabbed my arm with its beak" or "The bird jabbed its beak on my arm."

The bird pierced my arm with its beak.

alternatively

The bird's beak pierced my arm.

Pierce To cut or pass through with or as if with a sharp instrument; stab or penetrate.

Neither jab nor peck necessarily imply the man's skin was broken, as requested by the OP.

Other suitable verbs used can be impaled or punctured.

Impale:

transfix or pierce with a sharp object

Puncture:

a small hole in something such as the skin, caused by a sharp object.