In order to close a short you must go to the market and acquire some securities to replace those you borrowed.

The acquired date is the date you closed the short sale.
The disposed date is the very same date if you closed at a profit.

For Stocks, the disposed date is two business days later (settlement) if you closed at a loss.

Note: Date Acquired and Date Disposed refer to Columns (b) and (c) on Form 8949 that you will report to the IRS.

Your trade date is the date you closed the trade and goes in (b). Settlement date must be calculated taking into account weekends and market holidays . 

References:

IRS Instructions for Form 8949,

"Column (c)—Date Sold or Disposed Of
Enter in this column the date you sold or
disposed of the property.
For a short sale, enter the date you delivered
the property to the broker or lender to
close the short sale."


However, If you have a gain, see also IRS Pub 550 Chapter 4.

"Exception for constructive sales. Entering
into a short sale may cause you to be treated as
having made a constructive sale of property. In
that case, you will have to recognize gain on the
date of the constructive sale. For details, see
Constructive Sales of Appreciated Financial Positions,
earlier."