This answer actually shows a fairly deep knowledge of the comic book source material, because Stephen Strange never officially involved himself in the events of Mark Millar’s Civil War comic.
When the conflict began, Strange admitted that he personally opposed the registration of superheroes, but by the time the fighting began, he had gone into seclusion in the arctic.
Rather than take a specific side in the battle, he quarantined himself, and fasted for forty days while meditating on the devastation of the war.
If Strange had been introduced to the Marvel Cinematic Universe before the events of the last Captain America film, we can likely assume that he would’ve done the same on the silver screen.