Here he is. James Brown listed at the bottom of the list below.
For further information, you will need to obtain his service record file, see the note at the top of this page.
Also, try searching through the many hits by doing a Goggle search, Orr's Rifles.
George Martin
10th Cavalry Regiment was organized in December, 1863, using M.L. Young's 11th Missouri Cavalry Battalion as its nucleus. It contained 559 officers and men. The unit served in C. Greene's and J.B. Clarke's Brigade, Trans-Mississippi Department, and skirmished in Arkansas and saw action in Price's Missouri Expedition. During this operation it reported 16 killed, 56 wounded, and 73 missing. The regiment was included in the surrender in June, 1865. Its commanders were Colonel Robert R. Lawther, Lieutenant Colonel Merritt L. Young, and Major George W.C. Bennett.
10th Missouri Cavalry CSA
This unit originally was Col. Emmett MacDonald's Missouri Cavalry Regiment. Due to casualities and MacDonald's death, it was reduced to become the 11th Missouri Cavalry Battalion under command of Lt. Col. Merritt L. Young. In fall of 1863, after it increased back to regimental size, it was redesignated the 10th Missouri Cavalry and commanded by Col. Robert R. Lawther.
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J Graham Brown
Residence was not listed;
Enlisted as a Private (date unknown).
"H" Co. SC 1st Orr's Rifles Infantry
BROWN, J. Graham 1st Lt. H Orr's Regiment of Rifles Promoted from First Sgt. June 1862. Killed at Gaines Mill, June 1862. [http://www.geocities.com/Yosemite/6648/Orr_Marion.html]
Brown, J. Graham - Company H, Orr's Regiment, 1st Lt., Marion Co., in battle at Gaines Mill June 1862, Promoted from 1st Sgt June 1862
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John L. Brown
Residence was not listed;
Enlisted as a Private (date unknown).
"D" Co. SC 1st Orr's Rifles Infantry
Brown, J. L. Company D, Orr's Regiment, Private, Anderson,[killed/died?] in battle at Jones Farm, 24 Sep 1864 [http://www.rootsweb.ancestry.com/~scwbts/surnames/b.htm#BRO]
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John P. Brown
Residence was not listed;
Enlisted as a Private (date unknown).
"D" Co. SC 1st Orr's Rifles Infantry
Brown, J. P. Company D, Orr's Regiment, Priv Anderson Transferred 1862
[http://www.rootsweb.ancestry.com/~scwbts/surnames/b.htm#BRO]
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Brown, J. - Co. E, 2nd SC, died Point Lookout prison, #3658, Listed on Point Lookout Prison Camp For Confederates monuments Point Lookout
Brown, Jesse J. - 1st, Co. L, Sgt., South Carolina, Elmira, #572
Brown, F. P. - Company D, Orr's Regiment, Private, Anderson, died in battle at Fredricksburg
Brown, James - Company E, Orr's Regiment, age18 when enlisted, Private, died in battle at Fredricksburg
[http://www.rootsweb.ancestry.com/~scwbts/surnames/b.htm#BRO]