Programmable gene integration in human cells has the potential to enable mutation-agnostic treatments for loss-of-function genetic diseases and facilitate many applications in the life sciences. CRISPR-associated transposases (CASTs) catalyze RNA-guided DNA integration but thus far demonstrate minimal activity in human cells. Using phage-assisted continuous evolution (PACE), we generated CAST variants with >200-fold average improved integration activity. The evolved CAST system (evoCAST) achieves ~10 to 30% integration efficiencies of kilobase-size DNA cargoes in human cells across 14 tested genomic target sites, including safe harbor loci, sites used for immunotherapy, and genes implicated in loss-of-function diseases, with undetected indels and low levels of off-target integration. Collectively, our findings establish a platform for the laboratory evolution of CASTs and advance a versatile system for programmable gene integration in living systems.