Short answer: I don't know of any, and haven't been able to find any.
Longer answer: the Hebrew word is דלת (d-l-th), pronounced délet in Modern Hebrew. Strong derives it from a root דלה (d-l-h) meaning "to swing"; Wiktionary doesn't link it to a root and instead says it goes back to Proto-Semitic *dalt "door". It seems to be cognate with Akkadian daltu and Aramaic dalthā, which means regardless of anything else it's probably inherited rather than loaned.
The Arabic equivalent of Hebrew d-l-th would be d-l-t; Hebrew lost the Proto-Semitic
/θ/ (merging it into
/ʃ/) and then gained it back through a sound change called "begadkefat spirantization". Arabic on the other hand kept almost all the original consonants and didn't do begadkefat spirantization. Long story short, a th in Hebrew (without exception?) corresponds to a t in Arabic.
Unfortunately, I've never heard of an Arabic word with the consonants d-l-t, and searching for دلت shows nothing relevant. If Strong is right, the root was actually d-l-h, but a search for that shows nothing relevant either.
Therefore, I feel relatively confident in saying that this root did not survive in Arabic.