ClearAll[ellipsoid]
ellipsoid[center_, {majorradius_, minorradius_}, angle_] := GeometricTransformation[
Ellipsoid[center, {majorradius, minorradius}], RotationTransform[angle, center]]
Examples:
Graphics[{EdgeForm[{Thick, Blue}], Opacity[.75], LightBlue,
ellipsoid[{0, 0}, {2, 1}, Pi/3], Opacity[1], Red, Point[{0, 0}],}]

SeedRandom[1];
centers = RandomReal[50, {50, 2}];
radii = RandomReal[{1, 5}, {50, 2}];
angles = RandomReal[{0, 2 Pi}, 50];
colors = RandomColor[50];
Graphics[{EdgeForm[{Thick, #}],
Opacity[.75], #, ellipsoid@##2, Opacity[1], Black, Point@#2} & @@@
Transpose[{colors, centers, radii, angles}]]

Graphics[GeometricTransformation[Ellipsoid[center, {major, minor}], RotationTransform[angle, center]]
? $\endgroup$