Efficient Algorithm Linear Temporal Logic to Deterministic Rabin Automata
There is a very recent tool to translate from LTL directly to deterministic Rabin automata. It can be obtained here: 

https://www7.in.tum.de/~sickert/projects/ltl2dra/

The page not only contains a link to the downloadable implementation, but also has link to a technical report that describes the construction for the translation. Apparently, a peer-reviewed paper about the construction has not appeared yet. Note that the construction is rather involved - the paper has 50 pages, and there is a reason why for many years, the detour though Büchi automata was (and somewhat still is) state-of-the-art.

Note that the computational complexity of the direct translation is not better than the one that one can obtain by translating LTL to non-det. Büchi automata and then applying Safra's method.