Can you cite unpublished opinions in federal court? (FRAP 32.1)

Short answer. In a federal court of appeals, yes, for any federal decision issued on or after January 1, 2007. Fed. R. App. P. 32.1 stops a circuit from banning or limiting those citations. But that rule only settles whether you may cite the decision. How much it counts is up to the issuing circuit, and every circuit rule we checked says its recent unpublished decisions are not binding precedent. Older decisions and district court filings follow other rules.

What FRAP 32.1 does [Requirement]
A court "may not prohibit or restrict the citation" of federal opinions, orders, judgments or other written dispositions designated "unpublished," "not precedent" or the like, as long as they were issued on or after January 1, 2007. Fed. R. App. P. 32.1(a).
When no publicly accessible electronic database has the decision, you must file and serve a copy along with the brief or other paper that cites it. Fed. R. App. P. 32.1(b).
The rule took effect December 1, 2006.

What it does not do: decide the weight [Jurisdiction-specific]
Each circuit sets the weight of its own decisions:
Second Circuit: rulings by summary order carry no precedential effect. 2d Cir. R. 32.1.1(a).
Ninth Circuit: unpublished dispositions and orders are not precedent, though they still count for law of the case and for claim and issue preclusion. 9th Cir. R. 36-3(a).
Tenth Circuit: unpublished decisions are not precedential, but you may cite them to persuade, and also for law of the case and for claim and issue preclusion. 10th Cir. R. 32.1(A).
Fifth Circuit: unpublished opinions from January 1, 1996 on are not precedent outside uses like res judicata or law of the case. Unpublished opinions issued before 1996 are precedent. 5th Cir. R. 47.5.3, 47.5.4.

Decisions from before 2007 [Jurisdiction-specific]
FRAP 32.1 does not reach them, so the circuit rules control, and they differ.
The Ninth Circuit's courts won't take citations to its pre-2007 unpublished dispositions, with three exceptions: law of the case and preclusion; factual uses such as showing double jeopardy, notice or a related case; and pointing out a conflict when you ask the court to publish a disposition or to rehear a case. 9th Cir. R. 36-3(c).
The Second Circuit allows its pre-2007 summary orders only for narrow uses: later proceedings in the same case or in a related one, estoppel and res judicata, and subsequent history. 2d Cir. R. 32.1.1(b)(2).
The Tenth Circuit lets you cite its pre-2007 unpublished decisions just as you would later ones. 10th Cir. R. 32.1(C).

District courts [Jurisdiction-specific]
FRAP 32.1 is an appellate rule, so in a district court look first at that court's local rules and the judge's standing orders. Circuit rules can reach the district courts too: the Ninth Circuit's rule speaks of citing its decisions "to the courts of this circuit." 9th Cir. R. 36-3(b), (c).

Copies, links and service [Jurisdiction-specific]
Fifth Circuit: when you don't need to supply a copy, you must give a citation to a publicly accessible electronic database. 5th Cir. R. 28.7.
Tenth Circuit: a decision not in a public database is attached to the filing and sent to all other counsel and self-represented parties. 10th Cir. R. 32.1(B).
Second Circuit: if you cite a summary order, give a copy to any party who has no lawyer. 2d Cir. R. 32.1.1(d).

Common mistakes
Reading FRAP 32.1 as making unpublished decisions binding. It only lets you cite them.
Citing a pre-2007 unpublished Ninth Circuit disposition to a court in that circuit for its reasoning.
Assuming FRAP 32.1 governs a district court brief.
Skipping the copy when the decision isn't in a publicly accessible database.

Read more
The Cases chapter (its opening is free to read): https://citationcode.com/book/cases (opens in a new tab)
Federal court rules on citations and filings, each linked to its official text: https://citationcode.com/court-rules/federal (opens in a new tab)