Technically, Indian Territory could not vote for secession as it was not an admitted state (and had no constitution). The tribal governments within the territories could act independently, however, and they independently signed treaties with Albert Pike, who represented the Confederacy as its commissioner on Indian Affairs, in 1861.
Why would the tribal governments even want to be part of this conflict? The reasons were as individualistic as the tribes themselves. For example, the Choctaw and Chickasaw national governments were led by powerful men with both Southern white and Indian heritage. They had brought slave-holding into Indian Territory during the removal years of 1824 to 1842, and demanded protection of the slave system as they counted their prosperity in the amount of land they held and the amount of enslaved people who could work the land.
Other tribal leaders, such as those who led the Caddos and Wichitas, were rightfully wary of the newly elected Republican Party, which supported "free soil expansion" by non-Indian homesteaders within areas designated for the tribes. Lincoln was known to not be a friend to the Indians, and much of his politics disregarded native rights completely.* By 1861, Union soldiers had abandoned the federal forts in Indian Territory. While neither tribe trusted the Southerners nor the Texans, they were left with no other option but to join the Confederacy for protection against criminal gangs and tribal enemies.
The re-taking of forts in Indian Territory was one minor focus of Grant's Vicksburg campaign in the Civil War. To protect the Confederate forts, such as Fort Washita and Fort Towson (resurrected as "Camp Phoenix" by Confederates) in the Red River Valley, Albert Pike commissioned the building of Fort McCulloch in today's Bryan County in 1862. Situated along the Blue River and named for General Benjamin McCulloch, the fort also protected the road between Fort Washita and Fort Gibson - which by this time, was under Union control. However, the Battle of Honey Springs in 1863 in today's McIntosh County (Creek Nation) effectively removed any semblance of order in Confederate protections in Indian Territory. The Confederates, which included Chickasaw and Choctaw regiments under the command of Douglas Cooper, were defeated by James Blunt's forces, which included the all-volunteer First Kansas Colored Infantry.
The Confederate defeat allowed the Union to gain control of supply stations and forts in northern Indian Territory. Plunder by roving criminal gangs who sold cattle and supplies to the Union army threatened the civilian inhabitants. Thousands of civilians sought refuge around Fort McCulloch, Fort Washita, Fort Towson, and nearby Boggy Depot. Those who could afford the trip sent their families and slaves into northern Texas to wait out the war.
The Union army still had its sights on Texas, and planned several attacks in the Red River Valley in February 1864 as the first prong (simultaneously with the Camden Campaign in Arkansas) of the Red River Campaign that was gearing up in Louisiana. The Union troops, led by Charles Willet, engaged Confederate forces, led by Adam Nail, at Middle Boggy Creek. The Union wanted to take a "slash and burn" approach all the way to the Red River, but fell short of its goal when its troops simply left the battle site after executing the Confederate wounded. Though neither side prevailed in this short altercation, it had a fairly major impact: the Union stopped its attempts of penetrating into Texas from Indian Territory. This may have been to support a new tactic: going through Arkansas.
*Republican legislation passed during the Civil War paved the way for the brutal plains wars from 1862 to 1890 and the devastating tribal Reconstruction Treaties of 1866.