Sputnik in theory offers you a way of plugging in different captcha solutions, but at the moment there is only one option: ReCapatcha.
ReCaptcha
ReCaptcha is a captcha service. You can add it to your Sputnik with no effort at all:
Step One: Tnstall recaptcha:
./bin/luarocks --only-from=http://sputnik.freewisdom.org/rocks/earth install recaptcha
Step Two: Get your Recaptcha Keys
Go to recaptcha.net and get yourself a pair of API keys. I'll refer to them as PUBLIC and PRIVATE.
Step Three: Configure Sputnik
Set the following config parameters:
CAPTCHAMODULE = 'recaptcha' CAPTCHAPARAMS = { PUBLIC, PRIVATE}
It should look something like this:
CAPTCHAMODULE = 'recaptcha' CAPTCHAPARAMS = {
    "6LdcBAIAAA37AAAH705JU7ad31hHT9837276KO_prDaN",
    "6LdcBAIAAAAAAFz7j92783ij083728372727DMQQt5", 
},
replacing PUBLIC and PRIVATE with your private and public ReCaptcha keys.
You can also set your sputnik.ws / sputnik.cgi to something like this:
return sputnik.new_wsapi_run_fn{
   VERSIUM_PARAMS = { '/home/yuri/sputnik/wiki-data/' },
   BASE_URL       = '/sputnik.ws',
   CAPTCHA_MODULE = 'recaptcha',
   CAPTCHA_PARAMS = {
    "6LdcBAIAAA37AAAH705JU7ad31hHT9837276KO_prDaN",
    "6LdcBAIAAAAAAFz7j92783ij083728372727DMQQt5", 
   },
}
This will do two things: anonymous users will be required to enter captcha to edit and new users will be required to enter captcha to register.