Amazon S3 Recover Deleted File

If you have versioning enable, yes you can! On a versioned bucket, a delete action on a file does not really delete it but it adds a version with a "Delete Marker". You can delete the delete marker with the AWS CLI:

aws s3api delete-object --bucket yourbucket-name --key "yourfile" --version-id id_of_the_delete_marker

You can get all the files in the bucket with

aws --output text s3api list-object-versions --bucket yourbucket-name > files.txt

If you want to undelete all the files in the bucket you can try:

echo '#!/bin/bash' > undeleteScript.sh && aws --output text s3api list-object-versions --bucket yourbucket-name | grep -E "^DELETEMARKERS" | awk '{FS = "[\t]+"; print "aws s3api delete-object --bucket yourbucket-name --key \42"$3"\42 --version-id "$5";"}' >> undeleteScript.sh && . undeleteScript.sh; rm -f undeleteScript.sh;

According to the Amazon S3 Documentation:

Once deleted, there is no method to restore or undelete an object.

Just updating this question as I was looking for the answer:

You can add VERSIONING to S3 buckets now. This will cause S3 to keep versions of an object even after deletion. Full documentation: http://docs.amazonwebservices.com/AmazonS3/latest/dev/Versioning.html