That seems high. I get a lot smaller number, but maybe I've messed up some unit conversions. I'm using:
1 ton = 10^3 kg
1 g CO2 = 12/44 g of C (C == carbon, not Celsius)
Density of C is 2.2 g/cm^3
1 Texas = 6.95x10^5 km^2
Assuming those are right and I didn't botch any conversions between metric prefixes I get this: 10^9 tons CO2 x 10^3 kg/ton x 10^3 g/kg = 10^15 g CO2
10^15 g CO2 x 12/44 g C/g CO2 = 2.7x10^14 g C
2.7x10^14 g C x 1 cm^3 C/2.2 g C = 1.2x10^14 cm^3 C
6.9x10^5 km^2/Texas x 10^10 cm^2/km^2 = 6.9x10^15 cm^2/Texas
1.2x10^14 cm^3 C / (6.9x10^15 cm^2/Texas) = 1.7x10^-2 Texas cm C
Check: 1.7x10^-2 Texas cm C x 1 km / 10^5 cm = 1.7x10^-7 Texas km C
1.7x10^-7 Texas km C x 6.9x10^5 km^2/Texas = 1.2x10^-1 km^3 C
1.17x10^-1 km^3 C x 10^15 cm^3/km^3 x 2.2 gm C/cm^3 C = 2.57x10^14 gm C
2.57 gm C x 44 gm CO2/12 gm c x 1 ton/10^6 gm = 9.4 x 10^8 ton CO2 = 0.9 gigaton CO2
PS: the above is for 1 gigaton of CO2 since that is what emissions figures usually use. But if you were just talking about after capture and extraction of carbon, multiply the above by 44/12, giving 6.2x10^-2 Texas cm C.PPS: If we took all of the CO2 out of the atmosphere, the amount of carbon would be enough to cover to Texas to about 53 cm.