Good news — the sentence is correct!
Correct sentence: The rooster's crowing is a natural alarm clock, signaling a new day.
- Rooster's crowing means the crowing belongs to the rooster (we use 's to show belonging).
- is a natural alarm clock tells what the crowing is (this is the main idea of the sentence).
- , signaling a new day is extra information that explains what the crowing does. The comma is fine here. You can also write the sentence another way without the comma: The rooster's crowing is a natural alarm clock that signals a new day.
Try saying it out loud: it sounds natural and clear.