Yes, but you must file an Application for Asylum and for Withholding of Removal on Form I-589 within one year of your arrival to the United States.
Individuals who hold Temporary Protected Status (TPS) or who have been granted humanitarian parole may file for asylum after the one-year deadline following their arrival to the United States, as long as they file within a reasonable period after the deadline.
A small number of individuals may be excepted from the one-year deadline under a recent lawsuit (the Mendez-Rojas class action agreement). Individuals who previously crossed the border seeking asylum but who were stopped and not informed of their right to apply for asylum within one year of entry may qualify for an exception to the one-year limitation if they file notice with the immigration court or with USCIS before April 22, 2022. This exception is unlikely to apply to most recent Ukrainian migrants.
Anyone else who files an asylum application after they have been in the United States for more than one year must show that there were exceptional circumstances that prevented them from applying sooner, or that circumstances have changed and have given rise to an asylum claim that previously did not exist.