Non-commutative QED would lead to deviations from the Standard Model depending on a new energy scale A(NC) and a unique direction in space defined by two angles eta and xi. In this analysis, eta is defined as the angle between the unique direction and the rotation axis of the earth. The predictions of a tree level calculation for the process e(+)e(-) --> gammagamma are evaluated for the specific orientation of the OPAL detector and compared to the measurements. Distributions of the polar and azimuthal photon angles are used to extract limits on the energy scale A(NC) depending on the model parameter eta. It is shown that the time dependence of the total cross-section could be used to determine the model parameter xi if there were a detectable signal. This is the first experimental study of non-commutative QED at an e(+)e(-) collider. (C) 2003 Published by Elsevier B.V.