In The Unicode Standard, Osage script implementation is discussed in  Chapter 20 Americas.

The Osage script was encoded in The Unicode Standard version 9.0. The script is now encoded in the following block:

BlocksCharacter RangeAdded in Unicode VersionUnicode chart
Osage 104B0..104FF 9.0  U104B0.pdf

At one point there was an intention for the script to be unified with Latin. However, at UTC #140 the decision was made to encode it as a separate script ( L2/14-177).

A number of proposals for its inclusion have been submitted to the Unicode Technical Committee and WG2:

2014-02-20 Preliminary proposal to encode the Osage script in the UCS — Michael Everson ( WG2 N4548,  L2/14-068)

2014-07-30 Proposal to encode Latin characters for Osage — Michael Everson, Herman Mongrain Lookout, Cameron Pratt ( WG2 N4587,  L2/14-175)

2014-09-21 Final proposal to encode the Osage script in the UCS — Michael Everson, Herman Mongrain Lookout, Cameron Pratt ( WG2 N4619,  L2/14-214)