Short Answer
Make a request with curl to https://www.howsmyssl.com/
<?php
$ch = curl_init('https://www.howsmyssl.com/a/check');
curl_setopt($ch, CURLOPT_RETURNTRANSFER, true);
$data = curl_exec($ch);
curl_close($ch);
$json = json_decode($data);
echo $json->tls_version;
that should output what TLS version was used to connect.
Digging Deeper
Curl relies on the underlying OpenSSL (or NSS) library to do the negotiation of the secure connection. So I believe the right question to ask here is what is the OpenSSL library capable of. If it can handle a TLS connection, then curl can handle a TLS connection.
So how to figure out what the openssl (or NSS) library is capable of?
<?php
$curl_info = curl_version();
echo $curl_info['ssl_version'];
which is going to dump out something like
OpenSSL/1.0.1k
Then you can go and have a look at the release notes for that version and see if it includes TLS support.
OpenSSL Release notes – https://www.openssl.org/news/changelog.html
NSS Release notes – https://developer.mozilla.org/en-US/docs/Mozilla/Projects/NSS/NSS_Releases
Spoiler Alert
- openssl includes support for TLS v1.1 and TLS v1.2 in OpenSSL 1.0.1
[14 Mar 2012] - NSS included support for TLS v1.1 in 3.14
- NSS included
support for TLS v1.2 in 3.15