Use the custom python function provided in the answer to this question, then divide by 12 to get inch:feet ratio.
Step 1: Add a text label to the print composer
Step 2: Insert an expression into the label
Step 3: Create a custom function
In the "Insert Expression" window, click the "Function Editor" tab. Click "New File," enter the file name get_composer_map_scale, click OK. Copy and paste the code on this page, then click "Load" to register the custom function.
Step 4: Use the custom function to display the scale as the ratio [inches on the page]:[feet in real life]
Copy/paste into your label:
1 inch = [%round(get_composer_map_scale( 'Composer 1')/12, 0)%] feet
Substituting the name of your print composer where it says Composer 1.
Note: I added the function round(value, places) to round to an integer value of feet. To display more digits, substitute the number of digits for the zero.
EDIT: This answer only works for QGIS 2. For QGIS 3, see this answer: gis.stackexchange.com/a/332759/35561. Thanks to @MrChe for the suggestion.