Here are some other ways to say it:
* Use one's connections
* Get someone to do a favor
* Intercede on someone's behalf
* Put in a good word for someone
For example:
* "I'm hoping my uncle can use his influence to get me an interview."
* "I'm so grateful you put in a good word for me with the manager."
The idiom "pull some strings" implies that someone has the power and ability to influence a decision or outcome, often by using their connections or relationships.