  Out-of-time-order correlator (OTOC), been suggested as a measure of quantum
information scrambling in quantum many-body systems, has received enormous
attention recently. The experimental measurement of OTOC is quite challenging.
The existing theoretical protocols consist in implementing time-reversal
operations or using ancillary quantum systems, therefore only a few experiments
have been reported. Recently, a new protocol to detect OTOC using statistical
correlations between randomized measurements was put forward. In this work, we
detect the OTOCs of a kicked-Ising model using this new measurement method on a
4-qubit nuclear magnetic resonance quantum simulator. In experiment, we use
random Hamiltonian evolutions to generate the random operations that are
required by the randomized OTOC detection protocol. Our experimental results
are in good agreement with the theoretical predictions, thus confirming the
feasibility of the protocols. Therefore, our work represents a step in
exploring realistic quantum chaotic dynamics in complicated quantum systems.
