No, Odo has never done such a thing, but Laas (another Changeling) has transformed his arm into a knife while standing beside Odo and then stabbed a Klingon. Odo has also allowed a weapon to pass through his head, and once transformed into a blob monster that attacked various people.
I've watched DS9 completely five times over the years, and have never seen such a scene. I've also worked my way through the bonus material and deleted scenes over the years and have never seen Odo do such a thing with his head.
That being said, in the Season 7 episode "Chimera", Odo discovers and befriends a Changeling by the name of Laas, who fashioned a long knife from his arm and then used it to stab a Klingon, with Odo standing next to him at the time:
This is perhaps the most violent thing that we see a Changeling do to a solid, and it is certainly the only weapon we have seen a Changeling fashion out of itself.
You friend could have been conflating Odo and Laas, and at the same time conflating this incident with one from the pilot episode "Emissary" (also pointed out by @Richard in a comment) where Odo had de-solidified his head to allow a weapon lobbed at him to pass through:
Finally, in the Season 2 episode "The Alternate", Odo had inadvertently transformed into a blob monster and had attacked several people, in particular Dr. Bashir, who gets "head butted" and is knocked to the floor — although it's hard to say which part of its body the Odo monster had used. Below, Dr. Mora is also attacked by Odo in this state:
We never get a really good look at the Odo monster (the image above is the best), but this concept art gives a good idea:
The Odo monster is as "badass" as it gets.