I think we can conclude that immigration for Muslims and Arabs is perhaps harder than it is for other people. I have a Muslim friend from Kuwait who is currently waiting for his green card, and you should hear the stories he has to tell about the joys of the US immigration system for him as a Muslim coming from the Middle East. However, overall, the statistics show a steady increase in the number of Muslims immigrating to the US.
On the other hand, I heard a report on NPR some time ago discussing how the immigration of Iraqis was being held up in a maze of red tape. This was, I believe, during the last administration. The thrust of the story was that Iraqis who had aided us during the war were at considerable risk for having done so, and they now wanted to emigrate, but were unable to do so. It seems to me that this might have had somewhat of a chilling effect.
A large number of Iraqis and Afghans immigrated her in the last decade as a direct result of the American occupations of those countries. For some, they were fleeing persecution because they had cooperated with the American Army or served as translators. Others were trying to escape the sectarian violence there. It is also easier to immigrate to the US if you have money, and a significant number of Iraq's wealthier families fled the country when things got bad from 2005 - 2007.
Most of the rest of the effects of US policies, in my opinion, have been on those 6.5 million Muslims who already resided in America on 9/11.
Immigration to the U.S. by Muslims has been influenced by U.S. policy in that the Refugee Act of 1980 authorizes the Office of Refugee Resettlement to set aside more that $100 million each fiscal year (e.g., $159 million in 2002) to facilitate the resettlement of refugees that include Muslims from many different lands, including such as Egypt and Afghanistan.
[See http://www.wnd.com/?pageId=15721, from which this response was drawn, for more specifics.]
The previous answers are all excellent. I suspect that another influence of U. S. government policy on such immigration has been the waging of two wars in Iraq and two wars (one by proxy forces) in Afghanistan. To the extent that some people from those nations have seen the U. S. as an ally, they may have wanted to come here. Also, to the extent that such wars have disrupted lives of people living in those countries, they may have wanted to emigrate. The U. S. has also been allied -- to various degrees -- with various middle eastern countries, such as Saudi Arabia and Egypt, and ties between such countries and the U. S. have probably also helped to foster immigration.
If any US policy led to an increase in Muslim immigration, it was the relaxation of immigration quotas in the 1960s. When this happened, the US became a destination for refugees and students, two major sources of Muslim immigrants. This contributed to one of the most powerful pulls for immigrants- the existence of established communities of people from a wide variety of Muslim backgrounds and ethnic groups.
According to a 2006 story in The New York Times, Muslim migration to the U.S. achieved record numbers just five years after the 9/11 attacks: 40,000 new Muslims were admitted in 2005, and 96,000 became permanent residents. In 2009, 115,000 Muslims became permanent citizens, and permanent residency status has increased about 2% each year since 1992.
I don't think that we know this for sure. But we could speculate, I suppose, that Arabs and Muslims have not immigrated to the US in very large numbers because they see the US in a negative light. Perhaps they feel that the US is anti-Muslim and don't want to come here.