The spin-magnetic moment of the proton $mu_p$ is a fundamental property of this particle. So far $mu_p$ has only been measured indirectly, analysing the spectrum of an atomic hydrogen maser in a magnetic field. Here, we report the direct high-precision measurement of the magnetic moment of a single proton using the double Penning-trap technique. We drive proton-spin quantum jumps by a magnetic radio-frequency field in a Penning trap with a homogeneous magnetic field. The induced spin-transitions are detected in a second trap with a strong superimposed magnetic inhomogeneity. This enables the measurement of the spin-flip probability as a function of the drive frequency. In each measurement the protons cyclotron frequency is used to determine the magnetic field of the trap. From the normalized resonance curve, we extract the particles magnetic moment in units of the nuclear magneton $mu_p=2.792847350(9)mu_N$. This measurement outperforms previous Penning trap measurements in terms of precision by a factor of about 760. It improves the precision of the forty year old indirect measurement, in which significant theoretical bound state corrections were required to obtain $mu_p$, by a factor of 3. By application of this method to the antiproton magnetic moment $mu_{bar{p}}$ the fractional precision of the recently reported value can be improved by a factor of at least 1000. Combined with the present result, this will provide a stringent test of matter/antimatter symmetry with baryons.
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