Yes, this can be done with help of certificates. I have an article on my
web site that describes this in detail:
http://www.sommarskog.se/grantperm.html.

However, this not at all sound right to me, at least if the user would
truncate the log file every day. Truncating the log is something you
only do in exceptional cases when there is an emergency. Normally, you
either:
1) Run with full recovery and schedule regular full backups as well as
  transaction log backups.
2) Run with simple recovery and schedule only full backups. The log
  will be auto-truncated.

When you run with full recovery, you do so, because you want to be able
to recover the database to any given point in time. But if you truncate
the log, you lose that possibility. Which in fact is self-evident in
SQL 2005, where the only way to do this is to set the database into
simple recovery.