Reducing the integer factorization problem to an NP-Complete problem
Just to be absolutely clear, Integer Factorization is not known to be NP-intermediate, just suspected to be based on the lack of either NP-completeness proof or polynomial-time algorithm (despite lots of work put into both). I don't know of any natural problem (i.e. not constructed by Ladner for the proof) that is definitely NP-intermediate if P and NP are different.

Okay, after that disclaimer, Graph Isomorphism is another likely candidate for a natural NP-intermediate problem. There's a simple polynomial-time reduction from it to Subgraph Isomorphism - just leave the graphs the same! Graph Isomorphism is just the special case of Subgraph Isomorphism where both graphs have the same size. The final touch is that Subgraph Isomorphism is NP-complete.

Apart from that, there is always of course the not-so-informative reduction promised by the  Cook-Levin Theorem, we known that any NP-intermediate problem has some nondeterministic polynomial-time Turing Machine that decides it, and we can convert this into an instance of SAT (just have to build the TM!).