Please read http://forum.remirepo.net/viewtopic.php?id=1966

Especially explain that you understand all the security issues.

You should rather switch to php 5.3.3 in base repo which is maintained by RH.

You don't have to rebuild anything.
libcurl in C6 support TLS 1.2

And from php-5.3.3-47 changelog

- add options to enable TLS in curl #1255920

And using any other version, just add, in you code

defined("CURL_SSLVERSION_TLSv1_2") or define("CURL_SSLVERSION_TLSv1_2", 6);

See https://github.com/paypal/TLS-update/issues/7

I don't understand what it doesn't work for you.

# cat /etc/centos-release 
CentOS release 6.8 (Final)

# rpm -q libcurl php-cli
libcurl-7.19.7-52.el6.x86_64
php-cli-5.3.3-47.el6.x86_64

# php -r '
>     $ch = curl_init();
>     curl_setopt($ch, CURLOPT_URL, "https://tlstest.paypal.com/");
>     curl_setopt($ch, CURLOPT_SSLVERSION, CURL_SSLVERSION_TLSv1_2);
>     var_dump(curl_exec($ch));'
PayPal_Connection_OKbool(true)

BTW, if you want to rebuild, you have to rebuild everything, not only libcurl, but also php, so php-devel won't help you.

+1 for gerjoremi
I'm using 5.6.28-1.el6.remi

php -i | grep SSL :
SSL => Yes
SSL Version => NSS/3.21 Basic ECC
core SSL => supported
extended SSL => supported
OpenSSL support => enabled
OpenSSL Library Version => OpenSSL 1.0.1e-fips 11 Feb 2013
OpenSSL Header Version => OpenSSL 1.0.1e-fips 11 Feb 2013
Native OpenSSL support => enabled

we have:
SSL Version => NSS/3.21 Basic ECC
it is a problem for example with the payment system 'stripe'. even using CURLOPT_SSLVERSION, CURL_SSLVERSION_TLSv1_2 is not working.

current work around is to update nss (yum update nss). but I guess it would be better to have ssl version using openssl instead of nss