Is it necessary that your partner (wife/husband) have English proficiency, when you are going to study abroad? I decided to go study Ph.D. in the United States. Is it necessary that my wife be good at English?

I am expressly interested in legal and statutory requirements of English proficiency for a spouse if I am going to be studying in the United States.
If you are in a large city or at a large university, then it probably isn't necessary. You will probably find a lot of people there, and their spouses, who speak your language, whatever it is. 

In a small town, however, it would be a different story, and your spouse might be a bit isolated without some language skills. 

There are many large State Universities throughout the country that have students and faculty from all around the world. When I was in grad school in such a place (long ago) I had neighbors from Iran, in fact. Some such large places have organizations for spouses of foreign faculty and students in which people can get together, though everyone tends to speak a different language. 

Also, many places, even small ones, have programs in secondary (and other) schools for English as a Second Language (ESL). These are taught by specialists. So, I think that no matter where you are, there would be opportunities to learn even if you didn't find people who speak your own language. 



As for the legalities, there is no requirement that a person be able to speak English. However, to become a citizen you need some minimal proficiency: http://pjclaw.net/uscitizenship/english-language-requirements-for-naturalization/. But you don't need proficiency on arrival and, since the process is long, there is an opportunity to learn. 

For the requirements to get a visa, see this site: http://www.ustraveldocs.com. But I note that there is no information there about Iran. The best place to get information is to visit a US consulate or similar place where visas are issued and get current requirements.