Can I use electric tape instead of soldering for Speakers?
Get a soldering iron already!  Or if this is really the only time you would ever use it, have someone with a soldering iron solder the wires for you as a favor.  With the right equipment, it should only take a minute or two.

You are also confusing means of making a connection with the means of holding that connection in place.  Solder does both these things.  Electrical tape only does the latter.  Therefore, no, electrical tape is not a substitute for soldering.

Not recommended

You can strip maybe &frac12; to &frac34; inch of insulation from each wire end.  Then run each wire thru the eyelet hole in the speaker lug, then twist it tightly around itself.  The twisting will tend to keep the wire in place, but it still won't make a great contact.

After you've done the best you can to electrically connect the wires with the speaker eyelets and to keep them there, you can wrap each connection in electrical tape.  That will protect the bare area from unintended electrical contact, and will help stabilize the kludgy joint mechanically.

While the above will largely work if done right, when the speaker is powered you can probably hear little crackling sounds as you pull on the wires or flex them around near the speaker.  Again, not recommended.