Abstract: Refugee integration is a central policy challenge for host countries, and where governments initially place refugees shapes their integration trajectories. Yet placement officers often have limited information about where each case is most likely to succeed. Algorithmic refugee matching uses administrative data, machine learning, and constrained optimization to recommend employment-optimized placements in real time as cases arrive, with human placement officers retaining final authority. Between January 2020 and June 2023, the Swiss State Secretariat for Migration randomly assigned about 2,000 refugee cases to receive a canton recommendation either algorithmically optimized for employment or drawn to approximate existing procedures, with placement officers and refugees blinded to assignment. The two arms used identical but separate canton and origin-group quotas, so gains reflect better refugee-canton matching rather than reallocation toward stronger labor markets. The trial began just before the COVID-19 pandemic shifted labor-market conditions. For the pre-registered primary outcome -- the share of months employed during the first three years -- the pooled intention-to-treat (ITT) estimate across the 2020-2023 placement cohorts was +2.2 percentage points (about 10% of the 22.3% control mean; 95% CI [+0.05, +4.33]), rising to +3.9 pp (about 17%; [+1.11, +6.68]) for the post-COVID 2022-2023 cohorts. Effects grew over time: at 36 months, the pooled ITT on the employment rate was +5.2 pp (about 11%; 95% CI [+1.10, +9.25]) -- comparable to the gains from hundreds of hours of intensive language training. Overall, the results provide rare field evidence that AI-based decision support can improve high-stakes public-sector allocation, offering a scalable, low-cost way to raise refugee employment.