hi! there is a little difference between these two phrases. if you want to be precise I will sing a song for you means that you will for someone as the song is dedicated to him/her i will sing a song to you means that you wil simply sing in presence of that preson but the song isn't espacially for him/her hope it helps :)

These two words are acceptable to use. However, if you wish to convey a specific meaning, you need to pay attention to how they are used in a sentence. "For" means that you want to benefit somebody when singing. "To", on the other hand, simply means you are just singing directly to them and not necessarily for their benefit.

I will sing a song for you. 我為你歌唱 I will sing a song to you. 我唱一首歌給你聽

Both are correct. I will sing a song /for/ you is more intimate (or personal). This is because you're singing for the sake of that person, instead of simply singing to them. Functionally, they are nearly equivalent. I would not worry very much about choosing one over the other.