We address the internal support against total free-fall collapse of the giant clumps that form by violent gravitational instability in high-z disc galaxies. Guidance is provided by an analytic model, where the protoclumps are cut from a rotating disc and collapse to equilibrium while preserving angular momentum. This model predicts prograde clump rotation, which dominates the support if the clump has contracted to a surface density contrast ≳10. This is confirmed in hydro adaptive mesh refinement zoom-in simulations of galaxies in a cosmological context. In most high-z clumps, the centrifugal force dominates the support, , where Vrot is the rotation velocity and the circular velocity Vcirc measures the potential well. The clump spin indeed tends to be in the sense of the global disc angular momentum, but substantial tilts are frequent, reflecting the highly warped nature of the high-z discs. Most clumps are in Jeans equilibrium, with the rest of the support provided by turbulence, partly driven by the gravitational instability itself. The general agreement between model and simulations indicates that angular momentum loss or gain in most clumps is limited to a factor of 2. Simulations of isolated gas-rich discs that resolve the clump substructure reveal that the cosmological simulations may overestimate by ∼30 per cent, but the dominance of rotational support at high z is not a resolution artefact. In turn, isolated gas-poor disc simulations produce at z= 0 smaller gaseous non-rotating transient clouds, indicating that the difference in rotational support is associated with the fraction of cold baryons in the disc. In our current cosmological simulations, the clump rotation velocity is typically more than twice the disc dispersion, Vrot∼ 100 km s−1, but when beam smearing of ≥0.1 arcsec is imposed, the rotation signal is reduced to a small gradient of ≤30 km s−1 kpc−1 across the clump. The velocity dispersion in the simulated clumps is comparable to the disc dispersion so it is expected to leave only a marginal signal for any beam smearing. Retrograde minor-merging galaxies could lead to massive clumps that do not show rotation even when marginally resolved. A testable prediction of the scenario as simulated is that the mean stellar age and the stellar fraction of the clumps are declining linearly with distance from the disc centre.