Yes. Select Analyze ► Distribution. When the results window appears, click on the inverted red triangle menu next to the column name and select Save ► Ranks or Ranks Averaged.
Alternatively, select the column of interest, right click on the column ► New Formula Column ► Distributional ► Rank. This will generate a new formula column with the Rank by row of the observations in the column of interest.
[Previously JMP Note 35352]