You have to create a source bundle from your application, see details here: http://docs.aws.amazon.com/elasticbeanstalk/latest/dg/applications-sourcebundle.html (Or alternatively you can use AWS CodeCommit or AWS CodeBuild as source for your application.)
Then you can use the AWS CLI to create a new version from your application and deploy it to one application environment. (See the CLI documentation for EBS here.)
Create a source bundle:
zip MyCodeBundle.zip <source files>
Upload that to S3:
aws s3 cp MyCodeBundle.zip s3://a-bucket-where-you-store-your-source-bundles/
Create a new application version using the source bundle you just uploaded:
aws elasticbeanstalk create-application-version --application-name YourEBSAppName --version-label YourVersionLabel --source-bundle S3Bucket="a-bucket-where-you-store-your-source-bundles",S3Key="MyCodeBundle.zip"
And finally you update one of your environments to use that version (this is deploy even though that verb is completely missing from the new AWS CLI for EBS - this was a little confusing for me):
aws elasticbeanstalk update-environment --application-name YourEBSAppName --environment-name YourEBSEnvironmentName --version-label YourVersionLabel