The six-dimensional potential energy surface of the X³Σ^-_g electronic ground state of B₂H₂ was determined using spin-unrestricted explicitly correlated coupled cluster methodology. The analytic representation of this surface was used to compute the rovibrational energies of this boron hydride dimer. For the ¹¹B₂H₂ species, the antisymmetric B-H stretching frequency is computed at 2693.2 cm^-1 and an isotopic shift of +10.7 cm^-1 is deduced for ¹⁰B₂H₂. Comparisons with the electronic ground state of diatomic fragments B₂ and BH are discussed. The J = 1 <- 0 rotational transition is calculated at 50511.5 MHz for ¹¹B₂H₂ and at 53551.0 MHz for ¹⁰B₂H₂. Spectroscopic constants of the deuterated isotopologues are reported.