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to give or allocate; allot:
to assign rooms at a hotel.
to give out or announce as a task:
to assign homework.
to appoint, as to a post or duty:
to assign one to guard duty.
to designate; name; specify:
to assign a day for a meeting.
to ascribe; attribute; bring forward:
to assign a cause.
Law. to transfer:
to assign a contract.
Military. to place permanently on duty with a unit or under a commander.
Law. to transfer property, especially in trust or for the benefit of creditors.
Usually, assigns. Law. a person to whom the property or interest of another is or may be transferred; :
my heirs and assigns.
Contemporary Examples

In the absence of facts, it is always easy to jump to conclusions; to find bread crumbs and assign a malevolent purpose.
Titillation Over Tiffany’s Lauren Ashburn May 27, 2011

White House officials often assign to President Obama a series of sports metaphors.
Government Shutdown Endgame: Last Minute Strategy Details Daniel Stone April 7, 2011

Make a list of chores and responsibilities in and around the house and assign them.
10 Tips to Start the Fall Off Right Barbara Guggenheim, Nadine Schiff September 4, 2010

Girls are directed through several pages of this until they are asked to assign the guy a series of pre-decided adjectives.
Meet Lulu: An App That Lets Girls Rate Guys Anonymously Isabel Wilkinson August 21, 2013

Why does it seem so reckless to assign an obsolete airplane to such a prominent mission?
Poland’s Deadly Decision Clive Irving April 9, 2010

Historical Examples

He was introduced to the boys, and then took them off to assign them their rooms.
The Rover Boys at Colby Hall Arthur M. Winfield

It is perhaps too early to assign him his place in American literature.
The Works of Whittier, Volume VI (of VII) John Greenleaf Whittier

It is employed here in contradistinction to physicians, and I have not ventured to assign a modern equivalent.
Early Travels in Palestine Arculf et al.

And if it be impossible to assign any, this will serve to confirm our suspicion.
An Enquiry Concerning Human Understanding David Hume

The mind is also able to look at these perceptions, to assign them a meaning and to reflect upon them.
Applied Psychology: Driving Power of Thought Warren Hilton

verb (mainly transitive)
to select for and appoint to a post, etc: to assign an expert to the job
to give out or allot (a task, problem, etc): to assign advertising to an expert
to set apart (a place, person, time, etc) for a particular function or event: to assign a day for the meeting
to attribute to a specified cause, origin, or source; ascribe: to assign a stone cross to the Vikings
to transfer (one’s right, interest, or title to property) to someone else
(also intransitive) (law) (formerly) to transfer (property) to trustees so that it may be used for the benefit of creditors
(military) to allocate (men or materials) on a permanent basis Compare attach (sense 6)
(computing) to place (a value corresponding to a variable) in a memory location
noun
(law) a person to whom property is assigned; assignee
v.

c.1300, from Old French assiginer (13c.) “assign, set (a date, etc.); appoint legally; allot,” from Latin assignare “to mark out, to allot by sign, assign, award,” from ad- “to” (see ad-) + signare “make a sign,” from signum “mark” (see sign). Main original use was in English law, in transferences of personal property. General meaning “to fix, settle, determine, appoint” is from c.1300. Related: Assigned; assigning.