Is it better to say I will steal your heart. "Grab" your heart is not culturally correct. But its cute coming from a non-native.

I will grab your heart = I will make you feel a strong love (or something like love) for me very quickly. I something "grabs" you (symbolically) it captures your attention in a positive way. Grabbing someone's heart would be taken much more on an emotional level.

It is better not to use such sentences. Grab has many meanings. Among them several might be offensive if used. 1. Get hold of easily 2.Obtain illegally However, another meaning is capture the attention. So it is better to avoid this sentence.