Add a Lambda function target using an Amazon SDK

    public static void putCWTargets(CloudWatchEventsClient cwe, String ruleName, String functionArn, String targetId ) {

        try {
            Target target = Target.builder()
                .arn(functionArn)
                .id(targetId)
                .build();

            PutTargetsRequest request = PutTargetsRequest.builder()
                .targets(target)
                .rule(ruleName)
                .build();

            cwe.putTargets(request);
            System.out.printf(
                "Successfully created CloudWatch events target for rule %s",
                ruleName);

        } catch (CloudWatchException e) {
            System.err.println(e.awsErrorDetails().errorMessage());
            System.exit(1);
        }
    }

Create the client in a separate module and export it.

import { CloudWatchEventsClient } from "@aws-sdk/client-cloudwatch-events";
// Set the AWS Region.
const REGION = "REGION"; //e.g. "us-east-1"
// Create an Amazon CloudWatch service client object.
export const cweClient = new CloudWatchEventsClient({ region: REGION });

Import the SDK and client modules and call the API.

// Import required AWS SDK clients and commands for Node.js
import { PutTargetsCommand } from "@aws-sdk/client-cloudwatch-events";
import { cweClient } from "./libs/cloudWatchEventsClient.js";

// Set the parameters
export const params = {
  Rule: "DEMO_EVENT",
  Targets: [
    {
      Arn: "LAMBDA_FUNCTION_ARN", //LAMBDA_FUNCTION_ARN
      Id: "myCloudWatchEventsTarget",
    },
  ],
};

export const run = async () => {
  try {
    const data = await cweClient.send(new PutTargetsCommand(params));
    console.log("Success, target added; requestID: ", data);
    return data; // For unit tests.
  } catch (err) {
    console.log("Error", err);
  }
};
// Uncomment this line to run execution within this file.
// run();

// Load the AWS SDK for Node.js
var AWS = require('aws-sdk');
// Set the region 
AWS.config.update({region: 'REGION'});

// Create CloudWatchEvents service object
var cwevents = new AWS.CloudWatchEvents({apiVersion: '2015-10-07'});

var params = {
  Rule: 'DEMO_EVENT',
  Targets: [
    {
      Arn: 'LAMBDA_FUNCTION_ARN',
      Id: 'myCloudWatchEventsTarget',
    }
  ]
};

cwevents.putTargets(params, function(err, data) {
  if (err) {
    console.log("Error", err);
  } else {
    console.log("Success", data);
  }
});