Yes.  In 2021, Representative Sue Errington (D, District 34) introduced House Bill 1216.  The bill has been referred to the Committee on Elections and Apportionment.  This bill would permit, but not require, RCV to be used in local elections.  Each county, municipality or governing body of a school corporation would make its own decision whether to use RCV. 

Similar bills have been introduced in the Indiana Senate in 2018 (S. 400), 2019 (S. 306), and 2020 (S. 370).   For further information about these bills, please see the National Conference of State Legislators, State Elections Legislation Database, here.

In 2020, the Indiana GOP virtual convention used RCV voting to select the party’s State Attorney General candidate, among other candidates.  According to GOP Chairman Kyle Hupfer, a virtual convention with RCV was a way to “ensure delegate’s voices are heard” and keep them safe after the pandemic.  After the convention, Chairman Hupfer described the voting process as “very smooth and transparent,” and noted that the convention had “off the charts” participation.  For additional information, see this statement by Chairman Hupfer (reference to RCV at about 2:40.)

Here is an excerpt from a GOP video describing their use of RCV in 2020: