Abstract Protein side-chain packing (PSCP), the task of determining amino acid side-chain conformations, has important applications to protein structure prediction, refinement, and design. Many methods have been proposed to resolve this problem, but their accuracy is still unsatisfactory. To address this, we present AttnPacker, an end-to-end, SE(3)-equivariant deep graph transformer architecture for the direct prediction of side-chain coordinates. Unlike existing methods, AttnPacker directly incorporates backbone geometry to simultaneously compute all amino acid side-chain atom coordinates without delegating to a rotamer library, or performing expensive conformational search or sampling steps. Tested on the CASP13 and CASP14 native and non-native protein backbones, AttnPacker predicts side-chain conformations with RMSD significantly lower than the best side-chain packing methods (SCWRL4, FASPR, Rosetta Packer, and DLPacker), and achieves even greater improvements on surface residues. In addition to RMSD, our method also achieves top performance in side-chain dihedral prediction across both data sets.