It's "cut in line". We use the expression "cut in line" when someone unfairly goes in front of other people who are waiting in line.
It's "cut in line" (without the article "the"). We commonly use this expression when someone goes in front of other people who are waiting in line.
Peter got annoyed when a woman cut in line in front of him.
Alice had to wait in line for two hours.
Notice that we leave out the determiner to emphasize the verb (be, cut, stand, wait, etc.) rather than the noun. Nevertheless, you can introduce the article a/the or another determiner to identify or quantify the noun (line) in sentences like these:
The line is not progressing.
It's a short line.