Looks like the asf-soap-adapter isnt part of your deploy. Try using bundler and make sure your Gemfile has something similar to the following:

Then do a $ bundle install before you commit and push to Heroku.

As what you have said, I added the asf-soap-adapter to my gem file.and stills an error occurs. Below are the sample configuration of my gem file and the error.

Gem File:

source "http://rubygems.org"

gem 'asf-soap-adapter', :require => 'activerecord-activesalesforce-adapter'

gem 'rails','2.3.8'

ERROR:

C:\Ruby192\example\mckein>bundle install

Fetching source index for http://rubygems.org/

Using rake (0.8.7)

Using activesupport (2.3.8)

Using rack (1.1.0)

Using actionpack (2.3.8)

Using actionmailer (2.3.8)

Using activerecord (2.3.8)

Using activeresource (2.3.8)

Using builder (3.0.0)

Using facets (2.8.4)

Installing hpricot (0.8.3) with native extensions

C:/Ruby192/lib/ruby/1.9.1/rubygems/installer.rb:483:in `rescue in block in build_extensions': ERROR: Failed to build gem native extension. (Gem::Installer::ExtensionBuildError)

C:/Ruby192/bin/ruby.exe extconf.rbchecking for stdio.h... *** extconf.rb failed ***

Could not create Makefile due to some reason, probably lack ofnecessary libraries and/or headers.

 Check the mkmf.log file for moredetails.  

You may need configuration options.

Thank you very much for your help!

ok, this is a different error. It is failing on installing hpricot. You might want to check out some of the following links:

http://www.eggheadcafe.com/software/aspnet/36256636/ruby-192-and-hpricot-gem.aspx

Here is my Gemfile as well which should help. This deploys happily to Heroku and connects to Force.com. There may be some additional gems listed you may not use but I suspect your error is related to not specifying the facets gem.