sound card voltage input
That's right, the sample rate of most sound cards goes up to only 48 ksps. A 38.4 kbps signal would look badly jittery.
Some fancier sound cards go up to 96 ksps or even 192 ksps. The waveform would look better, but still jittery.
Also remember that most sound cards are AC coupled. An ordinary serial-port signal will probably appear sloped and bounce around a lot.
To check the sound card's input voltage range, you could simply apply a test signal (such as a 1 kHz sinewave) at various amplitudes, and watch for clipping in your sound recording program. Most sound cards will survive several times the clipping voltage without suffering damage, depending on the design quality.