It is not produced in the scope. It is displayed on the scope. So, unless you tell us something about the signal - amplitude, frequency, etc., you are on your own.
Yes you got what I meant, the signal displayed on the scope.
The ECG signal amplitude range is 0.05mV - 3mV
and it frequency range 0.01Hz - 300Hz
Given that the range of voltages that the Arduino can measure (slowly) on an analog pin is 0 to 5.0V (for 5.0V Arduinos), your voltages range from 1/100000th to 60/100000th of the range from 0 to 1023. The Arduino would need to return values from 0.0123 to 0.6138 to represent the signal that you want to input to it. Given that signal, the Arduino will consistently return 0.
Things are slowly coming under your control. Why are you diverting? @PaulS has been guiding/helping you; others will join soon to make your project successful.
So, you have fast (300 Hz compare to slowly varying DC) varying DC signal. You are sure that the signal is all along uni-polar -- the signal does not make an excursion below the 0V line. Check again the polarity of the signal by changing the coupling mode of the scope to AC.
You have said that the signal has gone through an instrument amplifier (IA). What is the signal level after the amplifier (the gain of the amplifier)? Do you have dual bias voltage (+ and -) for your IA? If not, what is the value of the single supply? What is the type number of your IA?
The frequency of the signal: 0.01 Hz to 300 Hz. Tell us, how often you need to sample/digitize it so that you will be able to reproduce the signal when it will be fed to the input of a DAC? Theoretically, it is ....... times; practically, it is .......... times.
You are saying that your SD Shield is of wireless type. Please, give a link to this shield.