It's usually phrased "take to the streets". Other options are "mount a protest/demonstration", "demonstrate", "picket" or "join a picket line".

In the U.S., we would most often use "take to the street" as part of a sentence, but not as a complete explanation of the events. "The people have taken to the street/streets in protest." A "demonstration" would usually (but not always) be a planned, more controlled protest, while "taking to the street" has an idea of an impromptu, emotional protest. This isn't always the case, but it is what I hear most often.