In 1918, the United States Army appointed its first Warrant Officers in the Army Mine Planter Service—a turn of events not without a certain degree of irony, given the fact that mine-planting is a task generally associated with the United States Navy, and the Navy had had Warrant Officers since the Revolutionary War. Although an Act of Congress designated Army Field Clerks and Field Clerks in the Quartermaster Corps as Warrant Officers, they wore the same uniform as the Mine Planter Service personnel (except their sleeves lacked the brown cuff of the Mine Planter Service officers).
Pre-2004 Warrant Officer Branch ItemsCongress created two grades of Warrant Officer in August, 1941, and in September of the next year the Army changed its regulations to authorize the insignia of grade for Warrant Officers other than those in the Mine Planter Service. The predominant colors used in the insignia were brown enamel and gold, a combination that was used until 1970 when Congress was considering expanding the number of Warrant Officer grade rather significantly.
As the branch color for Warrant Officers, brown was the color used for the hatband of the service cap and for the sleeve braids worn by Warrant Officers up until 2004, when the Army changed regulations and made Warrant Officers wear branch-specific colors.
Try to find out why brown was chosen as the color for the Warrant Officer Corps, however, and you run into some explanations that are bit far-fetched, to say the least. The overwhelmingly dominant account is that brown became the “official” color of the Corps because the Mine Planter Service personnel—originally 40 Warrant Officers in all, serving as Masters, Mates, Chief Engineers, and Assistant Engineers—used “brown strands from burlap bags” as insignia of rank before the Army created official rank insignia for them.
As hard as it is to picture in the mind's eye, this is the explanation given by CWO5 (retired) David P. Welsh of the Warrant Officer Historical Foundation, and in the absence of any other account it's probably true. And while it might be somewhat slim on precise details, it does surpass what we find on The Institute of Heraldry’s Web page for the Warrant Officer’s Collar Insignia: “Brown has been used as the color to represent warrant officers.”