"Ancient Rome" is a commonly used name to describe the civilization. Since we normally capitalize the names of civilizations we should capitalize the whole set of words "Ancient Rome". In other words, Ancient is considered part of the name.

Should the word ancient be capitalized?

Especially in older sources, the word “ancient” is sometimes capitalized in phrases like “ancient Greece,” “ancient Rome” and “the ancient world.” However, for most modern writers, all those phrases should take a lower-case letter.

Is Roman god capitalized?

Capitalize words referring to the Deity: God, the Almighty *The word god is not capitalized when it refers to gods of ancient mythology: Neptune was the Roman god of the sea.