There is a reduction from DL to RSA if the DL oracle accepts composite modulus. For prime modulus, the reduction is not known. I copied the following from this wikipedia page with minor edits.

Let $$n = pq$$ be RSA modulus.

1. Generate random number $$a$$ co-prime to $$n$$ and random number $$x < n$$ but very close to $$n$$.

2. Compute $$b = a^x \text{ mod } n$$ but don't tell $$x$$ to the 'discrete log oracle'.

3. Instead ask it to find the discrete log of $$b \text{ mod } n$$ (to base $$a$$). Let the value returned by the oracle be $$y$$.

4. There is a very high probability that $$y \neq x$$. If so $$x-y$$ will be a multiple of the order of $$a$$ which can easily be used to factor $$n$$. I will not go to the details of factoring once (a multiple of) the order of $$a$$ is known. (since this is a well known method, also used in Shor's algorithm). If we are unlucky and $$x=y$$, then we start over.