Absolutely, yes. But you'll need a frontend.
An EKG is usually just an instrumentation amplifier or a multistage amplifier with as many dB of common mode rejection as you can get.
The problem is that people are bags of electrolyte-rich fluids and meat with that right combination of resistance on the outside (skin) and relatively lower impedance to AC signals that all sorts of radiated EMI couples into our skin all the time.
If you've ever accidentally touched the tip of a speaker jack with your finger, or heck, just try probing your finger with your oscilloscope (isn't that the first thing one does with a new scope? I know it is for me!), you'll see what I mean. There is probably a volt or 2 of 50Hz or 60Hz ripple just from the wiring in your house.
This presents a problem when trying to detect electrical signals originating deep inside the skin-enclosed meat sack with all that noise coupling right at the surface trying to drown it out.
Where that noisy garbage coupling into your skin is on the order of a volt or two, the signals from your heart (at the point of detection on your skin at least) are about 1mV peak to peak. To get a good waveform, you'll want to be able to clearly see peaks as low as 20µV.
So you can't use an oscilloscope unaided, you can certainly use one as a very effective ECG/EKG with a front-end.
Such a front-end is not particularly difficult to make. The bandwidth and frequency of signals from the human heart are... quite slow in the context of analog electronics. This makes a frontend particularly forgiving, and you can even build one on a breadboard with just one IC.
Essentially, it all boils down to two things: You need a lot of gain, and a lot of common mode rejection.
Common mode rejection is achieved by, at the simplest, coupling the op amp's ground reference to your own body through a low (but not too low) resistor, like 100Ω. This is the lead that tends to connect far away from your chest, like at the angle or leg. This ensures only the noise gets picked up and rejected as common mode, leaving the cardiac signal (which are far too weak to matter that far away in your ankle or where ever).
A higher performance way of achieving this is to actually use a second op amp to drive the ground reference (your skin) and actively cancel out most of the common mode noise.
If you search for 'ECG frontend circuit', you'll find quite a few complete schematics of varying simplicity or complexity.
Any of them can work, but it ultimately depends on what level of performance is acceptable.
I have personally made this one, and a different similar one that also used a right leg driver that I can't seem to find, and both exceeded my expectations. They worked quite well:
Do not attach anything connected to your body like this to an oscilloscope that plugs directly into the wall. You must use an isolation transformer to fully isolate the oscilloscope so no ground path can be taken through you (and probably the electrical conduction system of your heart). Real ECGs are fully isolated if they plug into the wall at all.
Final note: Your body doesn't run on electric currents.
It runs on ionic current. Electric current has electrons as the charge carriers making up that current, but inside your body, it is positive ions rather than electrons that flow and do things like make your muscles move.
For that reason, you need to use some sort of electrolyte between an electrode and your skin, forming a half cell and allowing the ionic currents to be converted into electric currents for use with your ECG frontend.
Buying proper medical electrodes is ideal, but I can personally attest that tinfoil with some shampoo smeared on it can work in a pinch if you are really impatient to test what you made. Your results may vary.
Use an isolation transformer and don't get hurt or killed accidentally. Beyond that, this is actually a great project that isn't too hard or expensive to build if you're sufficiently interested and motivated. Good luck!