DreamHost and BitBucket SSH Key connection without prompting for passphrase

DreamHost and BitBucket SSH Key connection without prompting for passphrase

Originally based on this guide: Using Bitbucket for Automated Deployments
I have a repo set up on BitBucket with a POST hook pointing to the
deploy.php script on my web server. The only difference between my script
and the default code in the guide is the path on line 143:
$deploy = new Deploy('/home/my_username/my_domain.com');
As expected, the script runs whenever I push a commit to my origin repo on
BitBucket but it doesn't pull in any new commits. The 2 entries in the log
from lines 117 and 121 are:
INFO: Resetting repository... HEAD is now at 35272c4 Initial commit
INFO: Pulling in changes... HEAD is now at 35272c4 Initial commit
No matter how many times I push a new commit, this script will not detect
any new commits. But if I ssh to my web server and run git pull origin
master, it will ask for my passphrase and then will successfully pull in
all commits since the last pull.
Is it possible to set up this connection to avoid the passphrase prompt so
that it performs the git pull successfully?