  We use deep multi-epoch PSF photometry taken with the Visible and Infrared
Survey Telescope for Astronomy (VISTA) to measure and analyze the proper
motions of stars within the Galactic globular cluster 47 Tucanae (47 Tuc, NGC
104). The observations are part of the ongoing near-infrared VISTA survey of
the Magellanic Cloud system (VMC). The data analyzed here corresponds to one
VMC tile and covers a total sky area of 1.77 deg^2. Absolute proper motions
with respect to ~9070 background galaxies are calculated from a linear
regression model applied to the stellar positions in 11 epochs in the Ks
filter. The data extend over a total time baseline of ~17 months. We found a
median proper motion of the stars within 47 Tuc of (mu_a cos(d), mu_d) = (+5.89
+/- 0.02(stat) +/- 0.13(sys), -2.14 +/- 0.02(stat) +/- 0.08(sys)) mas/yr, based
on the measurements of ~35000 individual sources between 5' and 42' from the
cluster center. We compared our result to the proper motions from the newest US
Naval Observatory CCD Astrograph Catalog (UCAC5) which includes data from the
Gaia data release 1. Selecting cluster members (~2700 stars) we found a median
proper motion of (mu_a cos(d), mu_d) = (+5.30 +/- 0.03(stat) +/- 0.70(sys),
-2.70 +/- 0.03(stat) +/- 0.70(sys)) mas/yr. The values derived from the VMC
data are consistent with the UCAC5 result, and are close to literature
measurements obtained using HST. We combined our results with literature radial
velocity measurements and reconstructed the orbit of 47 Tuc, finding that the
cluster is on a low-ellipticity orbit and is confined within the inner ~7.5 kpc
of the Galaxy. We show that the use of an increased time baseline combined with
PSF-determined stellar centroids in crowded regions significantly improves the
accuracy of the method. In future works, we will apply this method to more VMC
tiles to study in detail the kinematics of the Magellanic Clouds.
