We use linear stability analysis to show that an isotropic phase of elongated particles with dipolar flow fields can develop nematic order as a result of their activity. We argue that ordering is favoured if the particles are flow-aligning and is strongest if the wavevector of the order perturbation is neither parallel nor perpendicular to the nematic director. Numerical solutions of the hydrodynamic equations of motion of an active nematic confirm the results. The instability is contrasted to the well-known hydrodynamic instability of an ordered active nematic.