There are many tools for VoIP calling available in the market. But still you need to pay something for that as well. Normally the people running a call centre setup use that for cheap calling for both domestic and international client.
The other effecfive method is calling through Skype. It gives you a $5 package to call to a certain country, for example $5 each for calling US and Germany. That could be helpful as well.
But first of all if outbound calling was not specified in the terms and conditions when the contract was started, you can discuss that with your client and ask him to get you the calling packages for VoIP/Skype.
I am sure there are excellent ways to solve your problem. Technical solutions.
But let's be very clear about one thing:
You are the freelancer.
You NEVER need to spend your own money on behalf of the client.
If the client is asking you to do work that requires you to use specialized equipment then the client can send you that equipment.
If you need to have a special account (such as a Skype business account), then the client can pay for that account.
The client can pay for things directly.
Or the client can use Upwork to send you funds (standard Upwork fees apply).
If the client needs a freelancer who has special equipment or software and that costs money, then the client may send that to you, pay for it, or hire somebody else to do that task. But as a freelancer you should never feel obligated to pay money for a client's project.