"Rooster sauce" is a nickname for Sriracha, a popular spicy chili sauce. It's called rooster sauce because the bottle of Sriracha has a rooster logo on it. Full definition
That's why I keep a bottle of Sriracha (aka Rooster sauce!!) (namelymarly.com)
You're Pronouncing Sriracha Wrong, and 6 Other Things You Didn't Know About Rooster Sauce. (pearltrees.com)
De Mars's Rooster Sauce Olympia, WA De Mars's olive oil base sets it apart from the more vinegary sauces, and its habaneros and jalapeños are chased with curry and garlic. (thrillist.com)