First of all you I would suggest not using char or str. Str is a built function/type and while I don't believe char would give you any problems, it's a reserved word in many other languages. Second you can achieve the same functionality using count, as in :
letterstring="This is a string!"
letterstring.count("i")
which would give you the number of occurrences of i in the given string, in this case 3.
If you need to do it purely for speculation, the thing to remember with recursion is carrying some condition or counter over which each call and placing some kind of conditional within the code that will change it. For example:
def countToZero(count):
print(str(count))
if count > 0:
countToZero(count-1)
Keep it mind this is a very quick example, but as you can see on each call I print the current value and then the function calls itself again while decrementing the count. Once the count is no longer greater than 0 the function will end.
Knowing this you will want to keep track of you count, the index you are comparing in the string, the character you are searching for, and the string itself given your example. Without doing the code for you, I think that should at least give you a start.