In The Unicode Standard, Kharoshthi script implementation is discussed in  Chapter 14 South and Central Asia-III: Ancient Scripts.

The Kharoshthi script was encoded in The Unicode Standard version 4.1. The script is encoded in the following block:

BlocksCharacter RangeAdded in Unicode VersionUnicode Chart
Kharoshthi 10A00..10A5F 4.1  U10A00

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

2002-09-19 Proposal to Encode Kharoṣṭhī in Plane 1 of ISO/IEC 10646 — Andrew Glass, Stefan Baums, Richard Salomon ( WG2 N2524,  L2/02-203)

2002-10-08 Proposal to add one combining diacritic to the UCS — Andrew Glass, Stefan Baums, Richard Salomon ( WG2 N2630,  L2/02-364)

2002-11-20 Supplementary Information to Accompany L2/02-203R2, Proposal to Encode Kharoshthi — Rick McGowan ( L2/02-424)

2003-09-18 Proposal to Encode Kharoṣṭhī in Plane 1 of ISO/IEC 10646 — Andrew Glass, Stefan Baums, Richard Salomon ( WG2 N2732,  L2/03-314)

2012-11-03 Sorting all RTL scripts together — Roozbeh Pournader ( L2/12-377)

2017-01-17 Additional Characters for Kharoṣṭhī Script — Andrew Glass, Stefan Baums ( L2/17-012)

Recommendations to UTC #150 January 2017 on Script Proposals ( L2/17-037) (See point 8.)

UTC #150 Minutes ( L2/17-016) (See C.2.1 for decision and action items)