One of my Client wants and API Integration so he is asking me my Public Ip so he can whitelist my address is it safe to give him?
Every web site you ever visit has your public IP.
It is typically safe to give it to a client.
If you are concerned about privacy and security, then you need an onion-routed and properly encrypted Virtual Private Network (VPN) to mask your public IP. And in that case, a client may not accept a VPN IP address to whitelist. Because, it would give anyone using that a similar exit node the same whitelist privileges. Generally, VPN exit nodes are communal. Unless, of course, the client or you have a private VPN, as well.