The Skp1-Cul1-F box complex (SCF) associates with any one of a number of F box proteins, which serve as substrate binding adaptors. The human F box protein βTRCP directs the conjugation of ubiquitin to a variety of substrate proteins, leading to the destruction of the substrate by the proteasome. To identify βTRCP substrates, we employed a recently-developed technique, called Ligase Trapping, wherein a ubiquitin ligase is fused to a ubiquitin-binding domain to "trap" ubiquitinated substrates. 88% of the candidate substrates that we examined were bona fide substrates, comprising twelve previously validated substrates, eleven new substrates and three false positives. One βTRCP substrate, CReP, is a Protein Phosphatase 1 (PP1) specificity subunit that targets the translation initiation factor eIF2α to promote the removal of a stress-induced inhibitory phosphorylation and increase cap-dependent translation. We found that CReP is targeted by βTRCP for degradation upon DNA damage. Using a stable CReP allele, we show that depletion of CReP is required for the full induction of eIF2α phosphorylation upon DNA damage, and contributes to keeping the levels of translation low as cells recover from DNA damage.