There’s built-in OpenVPN GUI in CyanogenMod since v4.2.15 and it’s poorly documented. When adding new VPN connection you have to tell which key you want to use and you can’t load anything from files. After few minutes of googling I found solution. Probably you have user.crt, user.key and ca.crt files generated with OpenVPN’s easy-rsa scripts. You can’t use them directly, you have to bundle certs and key into PKCS12 file. You need simply to run the following:

openssl pkcs12 -export -in [PathToClientCert] -inkey [PathToClientKey] -certfile [PathToCACert] -name [FriendlyName] -out certs.p12

Remember to replace [PathTo...] with proper filenames. [FriendlyName] will be displayed in certificate select dialog on your phone.

After that, upload file to your SD card and go to the Settings › Security and location, and select Import from SDcard. Now you can setup your OpenVPN connection.