SSH port forwarding should do the trick. Try running this from you client.
ssh -f -N -L 6379:<your redis node endpoint>:6379 <your EC2 node that you use to connect to redis>
Then from your client
redis-cli -h 127.0.0.1 -p 6379
It works for me.
Please note that default port for redis is 6379 not 6739. And also make sure you allow the security group of the EC2 node that you are using to connect to your redis instance into your Cache security group.
Also, AWS now supports accessing your cluster more info here
The previous answer was accurate when written, however it is now possible with some configuration to access redis cache from outside using the directions according to Accessing ElastiCache Resources from Outside AWS
Old Answer
No, you can't without resorting to 'tricks' such as a tunnel, which maybe OK for testing but will kill any real benefit of using a super-fast cache with the added latency/overhead.
The Old FAQ under How is using Amazon ElastiCache inside a VPC different from using it outside?:
An Amazon ElastiCache Cluster, inside or outside a VPC, is never allowed to be accessed from the Internet
However, this language has been removed in the current faq
Your system outside AWS ---> Internet --> HAProxy with public IP --> Amazon Redis (Elasticache)
Notice that there is another good reason to do that (at that time)
As we use node.js client, which don't support Amazon DNS fail over, the client driver don't support dns look up again.
If the redis fail, the client driver will keep connect to the old master, which is slave after failed over.
By using HAProxy, it solved that problem.
Now using the latest ioredis driver, it support amazon dns failover.