Short answer: you can
Long answer:
Unfortunately (for you but perhaps not for most folks) , the revision history for a deleted file is still there - it's just a little harder to get at.
Here's an example:
$ touch one
$ svn add one
$ svn ci -m "Added file one"
$ date >> one
$ svn ci -m "Updated file one"
$ date >> one
$ svn ci -m "Updated file one again"
$ svn log file:///repos/one
------------------------------------------------------------------------
r3 | andrewr | 2008-08-29 12:27:10 +1000 (Fri, 29 Aug 2008) | 1 line
Updated file one again
------------------------------------------------------------------------
r2 | andrewr | 2008-08-29 12:26:50 +1000 (Fri, 29 Aug 2008) | 1 line
Updated file one
------------------------------------------------------------------------
r1 | andrewr | 2008-08-29 12:25:07 +1000 (Fri, 29 Aug 2008) | 1 line
Added file one
------------------------------------------------------------------------
$ svn delete one
$ svn ci -m "Deleted file one"
$ svn up
$ touch one
$ svn add one
$ svn ci -m "Adding file one back in"
$ svn log file:///repos/one
------------------------------------------------------------------------
r5 | andrewr | 2008-08-29 12:29:13 +1000 (Fri, 29 Aug 2008) | 1 line
add one back
------------------------------------------------------------------------
It looks like it works (the old history is gone), but if you request the file at older revisions you get the history
of the deleted file.
$ svn log -r 3:1 file:///repos/one
------------------------------------------------------------------------
r3 | andrewr | 2008-08-29 12:27:10 +1000 (Fri, 29 Aug 2008) | 1 line
Updated file one again
------------------------------------------------------------------------
r2 | andrewr | 2008-08-29 12:26:50 +1000 (Fri, 29 Aug 2008) | 1 line
Updated file one
------------------------------------------------------------------------
r1 | andrewr | 2008-08-29 12:25:07 +1000 (Fri, 29 Aug 2008) | 1 line
Added file one
------------------------------------------------------------------------