convert string to time using culture info and store in SQL

New answer just using TimeSpan

The problem is that : isn't recognized within the custom TimeSpan format specifier. You need to escape it. At that point, the culture really isn't relevant at all, so I'd specify the invariant culture, personally:

TimeSpan result = TimeSpan.ParseExact(input, "hh':'mm':'ss",
                                      CultureInfo.InvariantCulture);

Personally I find it irritating that : isn't recognized... but that's a matter for the BCL team.

Original answer

Personally I'd use my Noda Time library, which aims to be a generally better date/time library for .NET. You can then parse it as a Duration, and convert that to a TimeSpan if you need to:

using System;
using NodaTime;
using NodaTime.Text;

class Test
{
    static void Main()
    {
        string input = "13:12:34";

        DurationPattern pattern = 
            DurationPattern.CreateWithInvariantCulture("H:mm:ss");
        // TODO: Consider error handling. The ParseResult<T> returned by
        // pattern.Parse helps with that.
        Duration duration = pattern.Parse(input).Value;
        TimeSpan timeSpan = duration.ToTimeSpan();
        Console.WriteLine(timeSpan);
    }
}

(Alternatively, you could just store the number of ticks in the duration.)

Note that I've used the invariant culture here - that's usually more appropriate when you're specifying an exact pattern.

You could use the current culture, but it would only affect the time separator (: in the invariant culture) in the pattern you're providing.