Is there a web site that I can go to research outstanding warrants in
Tacoma, Washington for the year 1987?

Not likley. Most warrants are for crimes that bear a statute of
limitations. When this time expires the warrants become "stale" and
are often recalled and cancelled. The record of the unserved warrant
being issued and recalled would likley be part of an law enforcement
agency's archived records but certainly not worthy of posting on the
internet some 16 years after the fact.

Intuition tells me that there is an un-asked question here. Is there
something else you are "really" wondering about perhaps?

Regards;
tutuzdad-ga