I don't see how getting an Islamic majority in the USA* by 1900 (or even 2015) is possible, but I think it's possible to get Muslims as a significant percentage of the US population by 1900, equivalent to Roman Catholics in OTL. Not easy, but possible.
The first thing you need to do is to give very large numbers of Muslims a reason for wanting to go to the USA, even though the people of the USA are alien in religion and culture. Second, you have to make it so that the mainly Protestant natives of the USA are not so bigoted against Muslims that they totally shut the door to Muslim immigration, the way they pretty much did to immigration from East Asia after the 1880s.
One way to get large-scale Muslim immigration to the USA would be for the European powers to be more aggressive and successful in conquering Islamic lands in the 19th century, and more aggressive in settling colonists there and either driving Muslims off their lands or trying to Christianize and Europeanize them. Perhaps the Ottoman Empire totally collapses in the early 19th century, the French and British and Russians move into North Africa and the Middle East earlier than OTL, and are more explicitly anti-Islamic. This would probably mean nasty guerrilla and anti-guerilla warfare across much of the area, but would also mean large numbers of Muslims willing to consider totally uprooting themselves and moving to a very foreign land. The USA, with a government that at least officially doesn't favor any religious group and doesn't persecute on the basis of religion, might look more attractive than most other options despite its distance and alien culture.
Now, how to get the mainly Protestant USA to accept these people? Well, I'm not totally sure about this one. If the Muslim immigrants are lucky, they won't be regarded in any more negative light than the Catholics and Jews who would probably also be immigrating in growing numbers as the 19th century goes on. In some ways, the aesthetics and practices of Muslims might even seem less alien to US Protestants than those of Roman Catholics. After all, most Protestants and most Muslims have a religious organization that is relatively decentralized, and where the clergy and religious leaders are seen more as guides and teachers than as intermediaries between God and humans. Also, both Muslims and many US Protestants were fiercely opposed to the use of images and figurative art in religious worship. Both Muslims and US Protestants heavily emphasized the centrality of their holy texts and preaching to worship. There are of course many, many big differences as well, but it's not impossible that some people on both sides will find common ground.
It's quite possible to envision a USA where by 1900 Muslims are roughly equal to Catholics in size and political and economic influence.
* I'm assuming that when the original poster refers to the "USA" they mean the same political entity as OTL, the one that declared independence from Great Britain in 1776 and adopted a stable constitution in the late 1780s. Of course, it's possible to have a plausible timeline where the same land that the USA occupies is occupied by a predominantly Islamic nation or nations, but this would not really be the "USA", and it would mean a POD long before the USA as a political unit existed.