Are Indian assistant professors eligible for tenure-track positions in the US?
Yes with caveats -- and the caveats have nothing to do with being Indian and everything to do with being outside of the American educational system:


There are particularities of the application process that are culturally bound and that you may not be familiar with (the style of the cover letter, its importance [or not], the style of your research and teaching statements, the format of your CV, who you ask to serve as a reference).
Your references may also be unfamiliar with American letters of reference styles. I find that foreign letters tend to be much shorter and much less enthusiastic.
Search committee members may not be familiar with your universities and its rank, with the ranking of the journals you've published in, and the significance of your teaching and service. They may be concerned that you do not know how to teach to American student audiences or that you may not be able to successfully apply for grants from American grant agencies.
The provost (who oversees searches) may be unwilling to authorize the search committee to bring in an international candidate due to the cost of airfare. 
The university may be concerned about whether or not you will be able to obtain a visa to work. Even if you are able to get a visa, even under the best of cases, an international candidate who accepts a job offer in March may not be able to start by August of the same year because of visa delays. This may have programmatic repercussions (i.e., they need someone to teach CS101 in the Fall).
Rarely, some jobs are closed to non-Americans because the government grants or cooperating agencies require security clearances or have other restrictions. This is more common in the engineering and physical sciences. 
In Canada, some positions are required to be offered to Canadian citizens before they are permitted to open to non-Canadians. The same rule technically applies in the USA for immigrant visas, but is not scrutinized as much.


etc.

As you can see, none of these have anything to do with you coming from India, and everything to do with being an international candidate. You'd have much more luck if you were applying from inside the USA (e.g., take a post-doc in the USA for a year or two and apply while on that).