I've searched Google and the GnuPG documentation and I haven't been able to find an answer. Some pointers in the right direction would be greatly appreciated.
The Tiger hash function is not part of the OpenPGP standard which GnuPG implements. A previous version of that standard (RFC 2440) had reserved an identifier for Tiger, but without actually standardizing it (no OID formally assigned). This was removed during elaboration of the next (current) version of OpenPGP, circa 2003, with apparent consensus, on the basis that having too many options may be detrimental to deployment and interoperability.
Older versions of GnuPG did implement the Tiger hash function, outside of the standard (by definition) but this was removed as well; apparently, the most recent version of GnuPG which still supported Tiger was version 1.2.6 (from 2004). So, to answer your question: right now, and for the foreseeable future, you do not user Tiger with GnuPG.
If you're looking for TIGER OID, it's 188.8.131.52.4.1.11591.12.2 . RFC 2440 doesn't specify OID, but GNU, the owner of 184.108.40.206.4.1.11591 OID, published it on their website. Does it account as being "formally assigned"?
So in essence the format is ready, but software is not.