(Microwave spectra of the four isotopologue/isotopomers, HI-(12)C(16)O(2), HI-(12)C(18)O(2), HI-(12)C(18)O(16)O, and HI-(12)C(16)O(18)O, have been recorded using pulsed-nozzle Fourier transform microwave spectroscopy. In the last two isotopomers, the heavy oxygen atom tilted toward and away from the HI moiety, respectively. Only b-type Ka = 1 <-- 0 transitions were observed. Spectral analysis provided molecular parameters including rotational, centrifugal distortion, and quadrupole constants for each isotopomer. Then, a four-dimensional intermolecular energy surface of a HI-CO2 complex was generated, morphing the results of ab initio calculations to reproduce the experimental data. The morphed potential of HI-(12)C(16)O(2) had two equivalent global minima with a well depth of 457(14) cm(-1) characterized by a planar quasi-T-shaped structure with the hydrogen atom tilted toward the CO2 moiety, separated by a barrier of 181(17) cm(-1). Also, a secondary minimum is present with a well depth of 405(14) cm(-1) with a planar quasi-T-shaped structure with the hydrogen atom tilted away from the CO2 moiety. The ground state structure of HI-(12)C(16)O(2) was determined to have a planar quasi-T-shaped geometry with R = 3.7717(1) A, thetaOCI = 82.30(1) degrees , thetaCIH = 71.55(1) degrees . The morphed potential obtained is now available for future studies of the dynamics of photoinitiated reactions of this complex.