Don't try using any general-purpose curve fitting algorithm for this.
The form of your function looks like a frequency response function, with the two unknown parameters $\omega_0$ and $\gamma$ - i.e. the resonant frequency, and the damping parameter. The function you specified omits an important feature if this is measured data, namely the relative phase between the "force" driving the oscillation and the response.
If you didn't measure the phase at each frequency, repeat the experiment, because that is critical information.
When you have the amplitude and phase data, there are curve fitting techniques devised specifically for this problem of "system identification" in experimental modal analysis. A simple one is the so-called "circle fitting" method. If you make a Nyquist plot of your measured data (i.e. plot imaginary part of the response against the real part), the section of the curve near the resonance is a circle, and you can fit a circle to the measured data and find the parameters from it.
In practice, a simplistic approach assuming the system only has one resonance often doesn't work well, because the response of a real system near resonance also includes the off-resonance response to all the other vibration modes. If the resonant frequencies are well separated and lightly damped, it is possible to correct for this while fitting "one mode at a time". If this is not the case, you need methods that can identify several resonances simultaneously from one response function.
Rather than re-invent the wheel, use existing code. The signal processing toolbox in MATLAB would be a good starting point - for example https://uk.mathworks.com/help/signal/ref/modalfit.html