If you can visit the U. S. Army Military History Institute, at Carlisle Barracks, Pa., you can view it there.

However, it is available for Inter Library Loan, see world.cat at:

https://www.worldcat.org/title/campaigning-with-parsons-texas-cavalry-brigade-csa-the-war-journals-and-letters-of-the-four-orr-brothers-12th-texas-cavalry-regiment/oclc/953500&referer=brief_results

It’s available at some 180 sites. Input your zip code which will list in accordance with distance from you