The parameters you have, i.e. offset, rotation and so on aren't a projection, they form an affine transformation from one Coordinate Reference System (CRS) to another. In OGC parlance, its an "engineering CRS". What it doesn't tell you is where in the world this transformation is relative to. For instance, Buckingham Palace is at coordinates
698359 5709414 in one CRS, and
529090 179645 in another (UTM zone 30N and OSGB36, respectively), yet they refer to the same geographical place.
The difference is the projection, that is how the Earth's spheroid is mapped to a plane. In the example above, both UTM and OSGB36 are transverse mercator projections, but UTM 30N's origin is on the equator west of Africa, and OSGB36's is south west of Scilly.
The part you need to find out then, is where in the world is the origin of your custom CRS, and which projection, if any*, was it in when it was digitised. Then you can just set that layer's projection in QGIS. The difficult part is actually applying your transformation parameters to your shape file because QGIS doesn't have scale and rotate tools, just translate/move! There is a feature request for rotate and scale, but it's not been looked at for a while. The CadTools plugin enables you to rotate a polygon about a vertex, but it lacks scaling.
*I say "if any" because long/lat coordinates aren't part of a projection, they're simply points on a sphere or spheroid (an equirectangular projection is perhaps the simplest because it directly maps longitude and latitude to x and y coordinates on a plane).