There are two possible scenarios,
If your application runs on .net framework 4.5 or less, and you can easily deploy new code to the production then you can use of below solution.
You can add the below line of code before making the API call,
ServicePointManager.SecurityProtocol = SecurityProtocolType.Tls12; // .NET 4.5
ServicePointManager.SecurityProtocol = (SecurityProtocolType)3072; // .NET 4.0
If you cannot deploy new code and you want to resolve the issue with the same code which is present in the production, then you have two options.
Option 1 :
[HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\.NETFramework\v4.0.30319]
"SchUseStrongCrypto"=dword:00000001
[HKEY_LOCAL_MACHINE\SOFTWARE\Wow6432Node\Microsoft\.NETFramework\v4.0.30319]
"SchUseStrongCrypto"=dword:00000001
then create a file with extension .reg
and install.
Note : This setting will apply at registry level and is applicable to all application present on that machine and if you want to restrict to only single application then you can use Option 2
Option 2 : This can be done by changing some configuration setting in config file. You can add either in your config file.
<runtime>
<AppContextSwitchOverrides value="Switch.System.Net.DontEnableSchUseStrongCrypto=false"/>
</runtime>
or
<runtime>
<AppContextSwitchOverrides value="Switch.System.Net.DontEnableSystemDefaultTlsVersions=false"
</runtime>