Is the phrase I came home at about one correct grammatically?

The phrase "I came home at about one" is grammatically correct. However, it sounds a bit awkward and could be improved. Here are a few ways to make it sound more natural:

* "I came home around one." This is a more common way to express a time that is approximate.

* "I came home at about 1 o'clock." This is a more formal way to express the time.

* "I got home around one." This is a more casual way to express the time.

Ultimately, the best way to say it depends on the context and the desired tone.