All of these sources point to July 23, 1862 as the date of Morgan's appointment as Colonel.

https://www.fold3.com/
compiled service records for Asa Morgan
July 23, 1862

Arkansas Confederate Regimental Histories
[This was Tom Ezell’s web site -now inactive]
26th Arkansas Infantry Regiment
Organized at Camp White Sulphur Springs near Pine Bluff from nine companies of "Morgan’s Battalion" between April and July of 1862 as the "3rd Trans-Mississippi Infantry Regiment", a tenth company was added to fill out to regimental strength and the unit renamed as the 26th Arkansas Infantry Regiment on its transfer to Confederate service on July 23, 1862 under the command of Colonel Asa S. Morgan.
Colonel Morgan was a veteran officer who had raised and commanded Company A of Fagan's 1st Arkansas Infantry Regiment in 1861, and when the 1st Arkansas was reorganized and consolidated with the 15th Arkansas after the battle of Shiloh, Morgan returned to Arkansas to raise another company of infantry at El Dorado, and Morgan was appointed by Maj. Gen. T.C. Hindman to command the new battalion and ultimately the regiment to which his company was assigned at Camp White Sulphur Springs.

http://www.couchgenweb.com/civilwar/26hisidx.html
26th Arkansas Infantry-
Organized as Morgan’s Battalion on June 14, 1862, it was increased to a full regiment and reorganized as the 26th Arkansas Infantry on July 23, 1862, at DeValls Bluff, Arkansas. Asa Stokely Morgan, formerly of the famed 1st Arkansas Infantry Regiment, was appointed as lieutenant-colonel of the battalion, and was promoted to colonel when the 26th Arkansas was organized.

NARA
RG 109
Chapter I, Volume 110 ½
A&IGO -- Roster of Officers of Maj. Gen. Sterling Price's Division, 1862-1863
Ark Infantry-A. S. Morgan-23 July 62-appointed by Hindman