This study proposes two new cointegration tests that employ rank-based and least absolute deviation techniques to create a robust version of the Engle-Granger cointegration test. Critical values are generated through a Monte Carlo simulation over a range of error distributions, and the performance of the tests is then compared against the Engle-Granger and Johansen tests. The robust procedures underperform slightly for normally distributed error terms but outperform for fatter-tailed distributions. This characteristic suggests the robust tests are more appropriate for many applications where departures from normality are common. One particular example discussed here is statistical arbitrage, a stock trading strategy based on cointegration and mean reversion. In a simple example, the rank-based procedure produces additional profits over the Engle-Granger procedure.