We investigate the effect of cooperative interactions in an ensemble of microorganisms, modeled as self-propelled disklike and rodlike particles, in a three-dimensional turbulent flow and show flocking and nematic ordering as an emergent phenomenon. Building on the work by Choudhary et al. [Europhys. Lett. 112, 24005 (2015)EULEEJ0295-507510.1209/0295-5075/112/24005] for two-dimensional systems, and combining ideas from active matter and turbulent transport, we show that nontrivial correlations between the flow and individual dynamics are essential for the microorganisms to flock in, for example, a turbulent three-dimensional marine environment. Our results may have implications especially in the modeling of artificial microswimmers in a hostile environment. © 2020 American Physical Society.