Yes, this functionality is part of the summarize function. When your field is defined as a Text field, the returned summary information is a frequency count for the selected field. Open the attribute table of the desired layer. Right click on the column you wish to count, and choose ‘Summarize …’. The dialog will allow you to add additional fields for summation, computing averages etc. If you don’t need any of this, leave the middle section blank. Make sure to create a file name that you will remember, the default name is ‘Sum_output’. If you have records selected in your table, you can choose to only generate summary statistics for those.
You will be prompted ‘Do you want to add the result table in the map?’. Click Yes.
The output table will contain a unique list of values for the selected field, and a Count column, indicating the number of times that value appears in the table. You might then wish to join this table to a shape file to use these frequency counts as a quantitative value on a map.