What is the time complexity for division by repeated subtraction?
Your algorithm makes exactly $\lfloor\frac{a}{b}\rfloor$ iterations of while loop.  

If we suppose that the size of the inputs is $n=max\{a,b\}$ then your algorithm will make at most $n$ iterations; when $a=n$ and $b=1$.  

Therefore, with this notation, your algorithm (on a high level) runs in $O(n)$ time complexity.



If you want to analyze it deeper, including the complexity of addition and subtraction which are $\Theta(n)$ for $n$-digit numbers, things get more complicated because $n$ we defined above was not the number of digits (decimal representation) but a value (unary representation).
As it can be shown, the base in which we represent numbers is not relevant, so the overall analyzed algorithm, having in mind also the properties of big-O and big-Theta runs in $O(n^2)$ where $n$ is the number of digits (in any base).