  We have measured the Faraday rotation of 62 extra-galactic background sources
in 58 fields using the CSIRO Australia Telescope Compact Array (ATCA) with a
frequency range of 1.1 - 3.1 GHz with 2048 channels. Our sources cover a region
$\sim 12\, \mathrm{deg}\, \times 12\,\mathrm{deg}$ ($\sim 1 $kpc) around the
Galactic Centre region. We show that the Galactic Plane for $|l| < 10^\circ$
exhibits large Rotation Measures (RMs) with a maximum |RM| of $1691.2 \pm 4.9\,
\mathrm{rad}\,\mathrm{m}^{-2}$ and a mean $|\mathrm{RM}| = 219 \pm
42\,\mathrm{rad}\,\mathrm{m}^{-2}$. The RMs decrease in magnitude with
increasing projected distance from the Galactic Plane, broadly consistent with
previous findings. We find an unusually high fraction (95\%) of the sources
show Faraday complexity consistent with multiple Faraday components. We
attribute the presences of multiple Faraday rotating screens with widely
separated Faraday depths to small-scale turbulent RM structure in the Galactic
Centre region. The second order structure function of the RM in the Galactic
Centre displays a line with a gradient of zero for angular separations spanning
$0.83^\circ - 11^\circ$ ($\sim 120 - 1500$ pc), which is expected for scales
larger than the outer scale (or driving scale) of magneto-ionic turbulence. We
place an upper limit on any break in the SF gradient of 66'', corresponding to
an inferred upper limit to the outer scale of turbulence in the inner 1 kpc of
the Galactic Centre of $3$ pc. We propose stellar feedback as the probable
driver of this small-scale turbulence.
