First, a note concerning using numeric values in SQL. Numeric values are used without single quotes. MySQL and some other DBMSes may accept quotes, but that isn't standard and portable SQL, IIRC.
Shouldn't you be joining the tables product and product_review on the product id column instead of category id?
Also, you might want to count the occurrences of the product id in the product_review table and not the category id. I think you don't even need to select the category as you already know it because you have chosen the products belonging to it.
Which DBMS are you using? Usually the group by clause must have the columns chosen in the select clause except the ones that are the result of an aggregate function (count, sum, max etc.).
Try something like this first, and then add columns you need for the final query (I used table aliases as it makes the code usually much shorter and clearer, IMHO):
SELECT P.prod_id, COUNT(PR.r_prod_id) AS total
FROM product P
LEFT JOIN product_review PR ON P.prod_id = PR.r_prod_id
WHERE P.r_cat_id = '$r_cat_id'
GROUP BY P.prod_id