A key question is whether your assault was "simple" or "aggravated"; the former is not considered to be a "crime involving moral turpitude," so it does not make you inadmissible.
Even if it were aggravated assault, a single conviction for a "crime of moral turpitude" does not by itself make you inadmissible if the maximum penalty you could have received was one year or less, and the actual penalty to which you were sentenced was six months or less.
For more information, see https://travel.state.gov/content/visas/en/general/ineligibilities.html.
The section that most concerns you is 212(a)(2)(A):
(A) Conviction of certain crimes.-
(i) In general.-Except as provided in clause (ii), any alien convicted of, or who admits having committed, or who admits committing acts which constitute the essential elements of-
(I) a crime involving moral turpitude (other than a purely political offense) or an attempt or conspiracy to commit such a crime, or
(II) a violation of (or a conspiracy or attempt to violate) any law or regulation of a State, the United States, or a foreign country relating to a controlled substance (as defined in section 102 of the Controlled Substances Act (21 U.S.C. 802)), is inadmissible.
(ii) Exception.-Clause (i)(I) shall not apply to an alien who committed only one crime if-
(I) the crime was committed when the alien was under 18 years of age, and the crime was committed (and the alien released from any confinement to a prison or correctional institution imposed for the crime) more than 5 years before the date of application for a visa or other documentation and the date of application for admission to the United States, or
(II) the maximum penalty possible for the crime of which the alien was convicted (or which the alien admits having committed or of which the acts that the alien admits having committed constituted the essential elements) did not exceed imprisonment for one year and, if the alien was convicted of such crime, the alien was not sentenced to a term of imprisonment in excess of 6 months (regardless of the extent to which the sentence was ultimately executed).
As you can learn at the bottom of CBP's ineligibilities page, even if your conviction exceeds these limits, you can still apply for a waiver of inadmissibility. Success is, of course, far from guaranteed.
As an aside, you are correct that an F-1 visa is a nonimmigrant visa. Nonimmigrants are indeed treated differently from immigrants in many respects, but the standards of admissibility are fundamentally the same.