In the past five years, droplet microfluidic techniques have unlocked new opportunities for the high-throughput genome-wide analysis of single cells, transforming our understanding of cellular diversity and function. However, the field lacks an accessible method to screen and sort droplets based on cellular phenotype upstream of genetic analysis, particularly for large and complex cells. To meet this need, we developed Dropception, a robust, easy-to-use workflow for precise single-cell encapsulation into picoliter-scale double emulsion droplets compatible with high-throughput screening via fluorescence-activated cell sorting (FACS). We demonstrate the capabilities of this method by encapsulating five standardized mammalian cell lines of varying sizes and morphologies as well as a heterogeneous cell mixture of a whole dissociated flatworm (5-25 μm in diameter) within highly monodisperse double emulsions (35 μm in diameter). We optimize for preferential encapsulation of single cells with extremely low multiple-cell loading events (<2% of cell-containing droplets), thereby allowing direct linkage of cellular phenotype to genotype. Across all cell lines, cell loading efficiency approaches the theoretical limit with no observable bias by cell size. FACS measurements reveal the ability to discriminate empty droplets from those containing cells with good agreement to single-cell occupancies quantified via microscopy, establishing robust droplet screening at single-cell resolution. High-throughput FACS screening of cellular picoreactors has the potential to shift the landscape of single-cell droplet microfluidics by expanding the repertoire of current nucleic acid droplet assays to include functional phenotyping.