Compelling evidence has been given for the high energy efficiency and update rates of neuromorphic processors, with performance beyond what standard Von Neumann architectures can achieve. Such promising features could be advantageous in critical embedded systems, especially in robotics. To date, the constraints inherent in robots (e.g., size and weight, battery autonomy, available sensors, computing resources, processing time, etc.), and particularly in aerial vehicles, severely hamper the performance of fully-autonomous on-board control, including sensor processing and state estimation. In this work, we propose a spiking neural network (SNN) capable of estimating the pitch and roll angles of a quadrotor in highly dynamic movements from 6-degree of freedom Inertial Measurement Unit (IMU) data. With only 150 neurons and a limited training dataset obtained using a quadrotor in a real world setup, the network shows competitive results as compared to state-of-the-art, non-neuromorphic attitude estimators. The proposed architecture was successfully tested on the Loihi neuromorphic processor on-board a quadrotor to estimate the attitude when flying. Our results show the robustness of neuromorphic attitude estimation and pave the way towards energy-efficient, fully autonomous control of quadrotors with dedicated neuromorphic computing systems.