Abarim Publications' online Biblical Hebrew Dictionary
The feminine noun דת (dat) is a loanword from Persian (the original word is data), and it means decree or law. Because it's Persian, it occurs only in the Book of Esther (Esther 1:19, 2:8, 4:3 and seventeen more places) and once in Ezra (Ezra 8:36). And because it refers to Persian law (which could be decreed by the king on whatever of his whims) it should not be confused with the Hebrew sense of Law, which only came from God.
Still, perhaps the Persian word for law could be so readily incorporated into Hebrew — truncated to דת (dt) instead of a more accurate דתה (dth) or even דתא (dt') — because it is identical to the Chaldean word דת (doth), meaning well or fountain.
In Deuteronomy 33:2 occurs the curious statement אשדת למו ('sdt lmw), which some translations explain to come from אשדה ('sdh), meaning mountain slope (NIV) but others interpret as אש דת למו ('s dt lmw), meaning a fiery law for them (KJV, JSP, ASV, Darby).