I am a citizen of Guyana who walked across the border from Mexico into the United States. I have no papers. My brother is a U.S. citizen and he filed a petition for me, but it will be years before my "visa number" comes up. Can I file an asylum claim?
In terms of basic legal procedures, you are allowed to file a claim for asylum even if you have other petitions pending with the U.S. government. There are advantages and disadvantages to filing an asylum claim while you are waiting for your immigrant visa, however, and you will have to weigh these carefully before deciding what to do.
First of all, since you didn't describe any basis for filing for asylum, we should start with a reminder that asylum cannot be viewed as a convenient way to extend your lawful stay in the United States. You should file an asylum application only if you have genuinely suffered or fear persecution in your country on account of your race, religion, nationality, membership in a particular social group, or political opinion. (In fact, someone who files a claim that is found to be "frivolous," that is, deliberately fabricated, becomes permanently eligible for a green card, per Section 208(d)(6) of the Immigration and Nationality Act.)
What's more, if the Asylum Office does not grant your request for asylum, it will refer you to an Immigration Judge for a hearing. Once in immigration court, you are at risk for being removed (deported) from the United States. This would not happen immediately, since there is a hearing and an appeals process, but you could eventually be sent home.
If you have, in fact, been persecuted or fear persecution, then of course you may have good reasons to apply for asylum. In fact, it may ultimately be better than applying through your brother, because you can win asylum even though you entered the United States without inspection.
If you wait until your visa number (based on the family petition filed by your brother) is current, you will not be able to get your green card in the United States unless the law changes. As it stands now, you would have to return to the U.S. consulate in your country for an immigrant visa interview – the last step in applying for lawful permanent residence. Depending on how much time you have been in the United States without legal status, however – which is likely to be at least ten years, given the long waits for visas in the F4 category for siblings of U.S. citizens -- leaving the U.S. might well bar you from returning for either three or ten years. With a grant of asylum, however, you could simply apply from a green card in the U.S. one year after approval.
If you decide to file an asylum claim, act quickly. You will need to apply within one year of your most recent entry into the United States unless there are exceptional or extraordinary circumstances in your case. (See Nolo's article, "Can I Still Apply for Asylum After the One-Year Filing Deadline?" for details.)
Strategic decisions like yours are often easier when you consult with an experienced immigration attorney. The attorney can sit with you and evaluate your potential claim for asylum and explain all the possibilities in detail.