What is the gerund phrase in Singing in the rain can get your shoes wet?
The gerund phrase is "singing in the rain", which is the subject of the sentence.
"Singing" is the gerund because it is being used as a noun. The sentence is not talking about a certain person who is singing in the ran, but the act of singing in the rain. Furthermore, the verb in the sentence is "can", and the subject always comes before the verb, so "singing" is the subject. Verbs, when they are used as subjects, are gerunds.