In the create plot window, you can also choose the Parametric notebook tab to create two dimensional parametric plots. This way you can plot a single parametric function. You can either specify the points as x and y, or giving a single complex number.
Here is an example of a parametric plot. Similar operations can be done on such graphs as can be done on the other line plots.
For plotting using the command line see the documentation of the LinePlotParametric or LinePlotCParametric function.