I can't find the correlation menu item, which is described in the documentation, in the statistics menu of my installed Origin. In pact, I only have the following item available: Analysis/Statistics/Descriptive Statistics and then there is no correlation coefficient there.
The "Correlation Coefficient" menu under "Statistics: Desc Stats" is only available in OriginPro. Please check your version again.
However, if you perform the linear fit ("Analysis: Fitting: Linear Fit" menu), the analysis report contains the "Pearson's r" (Pearson's correlation coefficient) in default.
If you need Spearman's rho and/or Kendall's tau for the rank data, you need the above mentioned "Correlation Coefficient" menu of Pro.