As others have noted, you will not be able to detect a star using an oscilloscope and an antenna. The received signal level is too low, and the oscilloscope not nearly sensitive enough.
A radio telescope consists of an antenna, an amplifier, and a receiver (that incorporates other amplifiers and other stuff besides - like filters and mixers to select the desired frequency range.)
An antenna by itself wouldn't pick up enough signal to be directly useful.
The oscilloscope lacks amplification and filtering needed to make the antenna signal useful.
As others have said, you can use commercial antennas and receivers to pick up the signals. There are kits you can buy with everything you need, or you can get the components piece at a time from various sources.
As an alternative, you might consider building a small radio telescope using standard satellite TV components.
I have one, and besides the sun and the TV satellites, it can detect the moon. I haven't gotten around to trying to detect smaller or less intense things. I do have it mounted on servos, though, and have made pictures of ambient RF signals. Houses and trees are surprisingly "bright" sources of 13GHz RF.
The folks here have instructions for building one, as well as examples of what you can do with it.
Here is another example of making such a small radio telescope.
I think both projects link back to the same original source.
You can usually get all of the needed parts at any store that sells satellite TV receivers. I bought my stuff on Amazon, but most of the hardware stores here stock those things as well.
All you need is a dish, an LNB, (both can be bought in a set) and one of the little gadgets that helps you aim the dish properly. And a few feet of cable and connectors, of course.
The dish has high gain.
The LNB contains amplifiers and filters to make the signal strong enough to be useful.
The alignment device is the final bit. It has yet more amplification, and converts the received radio signal to a (somewhat noisy) voltage that represents the strength of the received signal.
The signal strength indication is shown on a small meter. You can also open the box, and add a couple of wires - you can then connect that to your oscilloscope and see how strong the signal is that you are picking up from the sun or whatever. The two wires driving the meter are the correct place to connect to.
My profile picture is an image I made in my garage using my servo aimed satellite dish. Not terribly impressive, but that was made without any kind of additional "lighting." All just ambient RF.
If you have a fluorescent light, you can pick up 60Hz modulated RF by pointing just the LNB at the light. Fluorescent lights cause broadband RF interference, and the LNB can pick it up at 13GHz. The signal strength meter demodulates it, and you can see a nice 60Hz signal if you connect an oscilloscope to the meter.
My detector is a little more advanced than just the little meter. I built a controller out of an Arduino.
It uses a MAX2015 as a signal strength detector, and has a 24 bit analog to digital converter. It also has a chip to generate control signals for the LNB.
The LNBs can actually receive two bands, and can use horizontal or vertical polarisation. My controller lets me switch among the various combinations.
The Arduino operates the hardware (it also drives the servos,) makes measurements, and delivers results to my PC over the serial port. It also takes commands as to what to do. The smarts are all in the PC - an Arduino just hasn't got what it takes to build an image out of a bunch of measurements.