The contents of select dropdowns are either static or, in certain cases, dynamic.
By static I mean that, if you create a Types select custom field, for example, you manually specify the options and their display values, and these are stored as metadata in array form with the field.
By dynamic I mean that the dropdown options are determined by a query of some sort, for example if you are filtering by a category then the relevant category terms will be retrieved by a query and used to populate the select box.
A text field fits neither of these cases. I suspect that you want the select box to show any and all of the different entries that have been entered for the text field, but there is no means to do this.
If that is what you want to do then you might be better off using tags (unstructured text taxonomy terms) which fit the dynamic select box case.
Or, you can mimic the static case with your text field if there are a limited number of known values the text field might contain. When you go to insert the filter for your text field as a select box you have the option to manually enter the values which will show in the select box. See the attached screenshot...