The definition of a standardized residual is the residual values divided by the standard deviation of the residuals. Therefore all that has to be done, is to save the residuals from the regression platform you are using(i.e. Fit Y by X, Fit Model, etc.).
Then create a new column and in that column
specify the formula
<Saved Residual Column Name> / Col Std Dev(<Saved Residual Column Name>)
Then simply go to Graph builder and plot the Standardized Residual column against your X column.
Jim