Migrating data using entity framework, linq and recursion
The following code is O(n^2). More precisely, it's Theta(n^2) because it'll always be exactly n.

foreach (var personalWebsite in personalWebsites)
{
    // You can use a HashSet to eliminate the need for the inner loops, which
    // would reduce your computational complexity from Theta(n^2) to Theta(n) - see below
    foreach (var socialNetwork in socialNetworksStr)
    {
        // You could "convert" both of these to some kind of "normal form" (see below) to eliminate the need for the relatively inefficient "Contains" and enable the use of a HashSet
        if (personalWebsite.Url.Contains(socialNetwork))
        {
            socialNetworks.Add(new UserSocialNetworkDTO() { SocialNetworkId = (short)(Array.IndexOf(socialNetworksStr, socialNetwork) + 1), Account = personalWebsite.Url });
            personalWebsitesRemoved.Add(personalWebsite);

            // If you do stick with a loop here, presumably each personal web site only
            // matches one social media site, so you can break out of the loop here to
            // improve your computational complexity for this bit from Theta(n) to O(n)
        }
    }

    // Same comments as above
    foreach (var customSocialNetwork in customSocialNetworksStr)
    {
        if (personalWebsite.Url.Contains(customSocialNetwork))
        {
            customSocialNetworks.Add(personalWebsite);
            personalWebsitesRemoved.Add(personalWebsite);
        }
    }


You can reduce this to O(n) by reducing the URLs to some kind of "normal form" (e.g. http://www.linkedin.com/in/some.person would just be "normalized" to "linkedin.com") and building a Dictionary (hash table) or HashSet. This would reduce the computational complexity from Theta(n^2) to Theta(n).

Also, even if you do stick with the "inner" foreach loops, there's no need to iterate over all of the social network sites every single time; I assume that each personal web site can only match one social media site, so if you find one that it matches it reduces the computational complexity from Theta(n^2) to O(n^2).