That looks like it was drawn in base R, free software available from r-project.org. A quick call to 'plot' would produce that plot if given the necessary x, y data and labels, see '?plot' for further details. It's a line drawing so can be saved as a vector, which has no resolution in the traditional sense so can be scaled as necessary.
That being said if you only want to produce a scatterplot as a one time thing then similar results can be achieved using excel if you have access to it (though MS Office is not free). This would likely circumvent the steepish learning curve with R.