Can a jury find a defendant guilty on a charge for which the defendant was not arraigned?
For example, if a defendant is indicted on a charge of manslaughter can the jury convict him of murder?
A defendant cannot be found guilty on a charge for which the defendant was not arraigned, but this reality is a trivial matter whose sole practical effect is to prevent trials in absentia.
There is also a buried second question implicit in the example given but not actually stated in as many words:
Can a defendant be convicted of crimes for which an indictment or information is not secured?
The answer to that buried second question is no, subject to the exception that a defendant may be convicted of a lesser included charge relative to one for which an information or indictment is secured and upon which the defendant is arraigned. A lesser included charge is a crime for which all the elements must be established to prove the greater charge, but the converse is not true.
Thus, is someone is charged only with manslaughter in an indictment to which they plead not guilty, they cannot be convicted of murder. But, if someone is charged with murder in an indictment, to which they plead not guilty, they can be convicted of either murder or manslaughter which is a lesser included charge relative to a murder charge.
Basically, the criminal justice process goes through the following steps in a felony case (some of which may be omitted in misdemeanor and/or petty offense cases):
Someone is charged with a crime in a criminal complaint and arrested. These two events can occur in either order. If the complaint is made first, an arrest warrant will be issued by a magistrate and form the basis for a subsequent arrest and booking. If an arrest is made first, usually because a law enforcement officer has probable cause to believe a crime was committed, the criminal complaint will be drawn up once the defendant has been arrested and booked.
After both events in step 1 are complete, a first appearance of the defendant in person before a magistrate or judge is held in a matter of one to three days, or even a matter of hours, at which counsel is appointed if the defendant is indigent, the defendant is formally advised of the charges in the criminal complaint, and bail is set (or denied for cause or waived). Confusingly a first appearance is sometimes called an "arraignment on the complaint", but I am assuming that your question used the term "arraignment" in the predominant sense of an arraignment on an information or indictment.
Then, in felony cases (but not misdemeanors), the criminal complaint is reviewed for probable cause following a preliminary hearing and if probable cause is found to exist it is converted to an "information" (if the preliminary hearing is waived by the defendant, the complaint is automatically converted to an "information"); or a grand jury reviews the criminal complaint for probable cause and if probable cause is found to exist it is converted to an "indictment".
The defendant is arraigned in person on the information or indictment. In an arraignment, the defendant is formally informed of the charges in the information or indictment, and the defendant enters a preliminary plea to each of the charges in the information or indictment. This would typically take five minutes to half an hour, depending upon the number of charges brought.
Pre-trial proceedings (e.g. "discovery" and motion practice), if any, are conducted by the lawyers for the prosecution and the defense.
A trial is held (if the defendant demands it, before a jury).
Caveat: There are also more steps prior to the filing of a criminal complaint or arrest (related to searches, seizures and interrogations), and there are also more steps after the trial (related to sentencing, appeals and collateral attacks on convictions and the sealing of records and pardons and commutations), but none of those steps are pertinent to this question.
A jury trial would simply never be (definitively and officially) scheduled until an arraignment of the defendant was conducted. So, while it is true that a jury trial would not be conducted on charges in an indictment until the defendant is arraigned (i.e. until the defendant enters a plea to the probable cause screened charges), in the ordinary course, this is a trivial matter.
But, because criminal trials can only be conducted after a defendant has been arraigned in person, the only time that a defendant can be tried in abstentia (i.e. without being present at the trial), is when the defendant is arraigned and enters a not guilty plea or the equivalent, and then absconds after that points but before the trial is conducted.
(I'm not a complete expert on this, it may be necessary for the defendant to be present when the trial is commenced as well, but I don't need to know to answer this question.)
Also, while the requirement of an indictment by a grand jury for felonies exists in federal court under the U.S. Constitution, and in some state courts (mostly in the Eastern U.S.) under state constitutions, the U.S. Constitution permits a state to substitute a preliminary hearing giving rise to an "information" for a grand jury indictment if its state constitution permits.
My source for this post is a hard copy of the book Israel, Kamisar and LaFave, "Criminal Procedure and the Constitution" (1994). But, these basic principles have been in place unchanged for a very long time.