Inedependent Texas
Texas had been independent until 1845 since breaking free from Mexico in 1836. Now, Texas had had a long history of slavery, and was even exempted by Mexico when they implemented their slavery ban in 1930. Following independence African descendants rights were diminished and slavery laws deregulated, leading to a doubling in slaves from 1836 to 1840.
Joining the United States of America
Texas eventually sought to join the US, and was eventually annexed in 1845. However, Texas now had a small problem. The Missouri Compromise of 1820, prohibited slavery north of 36°30′ parallel north, which a small part of Texas was, thus preventing them from becoming a slave state.
The solution? Cut off the part above the 36°30′ parallel north. Texas proceeded to surrender this area in 1850. For 40 years it would be a no man’s land with no state or territorial ownership until it was assigned to Oklahoma in 1890.
Meanwhile, Texas enjoyed its status as a slave state, and from 1840 to 1860 the number of enslaved people in the state rose by 500%.
So, there you have it. The reason for the weird border between Texas and Oklahoma is due to Texas dearly wanting to be a slave state.