Yes, you can dye your hair while pregnant. Occasional hair coloring is unlikely to meaningfully increase the risk to the baby when the product is used as directed and applied to healthy, unbroken scalp skin. Research is limited, however, so it is not possible to say there is absolutely no risk.
Only small amounts of hair dye chemicals are expected to be absorbed through a healthy scalp. Studies have not shown a significant increase in birth defects with typical personal use, although some people may prefer to wait until after the first 12 weeks of pregnancy as an extra precaution.
When coloring your hair, wear gloves, use the product in a well-ventilated area, leave it on only for the recommended amount of time, and rinse the scalp thoroughly afterward. A patch or strand test can also be helpful because pregnancy may change how the skin or hair reacts to a product.
People who work regularly with hair dyes and other salon chemicals may have much higher and more frequent exposure. If this applies to you, or if you have concerns about can you dye your hair while pregnant, discuss your exposure with your OB-GYN or another prenatal healthcare professional.