Accurate and stable measurement of inertial quantities is essential in geophysics, geodesy, fundamental physics, and inertial navigation. Here, we present an architecture for a compact cold-atom accelerometer-gyroscope based on a magnetically launched atom interferometer. Characterizing the launching technique, we demonstrate 700–parts per million gyroscope scale factor stability over 1 day, while acceleration and rotation rate bias stabilities of 7 × 10−7 meters per second squared and 4 × 10−7 radians per second are reached after 2 days of integration of the cold-atom sensor. Hybridizing it with a classical accelerometer and gyroscope, we correct their drift and bias to achieve respective 100-fold and 3-fold increase on the stability of the hybridized sensor compared to the classical ones. Compared to a state-of-the-art atomic gyroscope, the simplicity and scalability of our launching technique make this architecture easily extendable to a compact full six-axis inertial measurement unit, providing a pathway toward autonomous positioning and orientation using cold-atom sensors.