Get current category ID of the active page-Collection of common programming errors
I found this question whilst looking for exactly what you asked. Unfortunately you have accepted an incorrect answer. For the sake of other people who are trying to achieve what we were trying to achieve, I thought I’d post the correct answer.
$cur_cat = get_cat_ID( single_cat_title("",false) );
As you said single_term_title("", false);
was correctly returning the category title, I’m not sure why you would have had troubles with your code; but the above code works flawlessly for me.