YES, you can use a scope as a curve tracer to measure the current gain in a transistor or the voltage gain in a FET or the transconductance of a MOSFET.
Simply use series resistor on emitter to monitor current and display as Channel 1 and Voltage as Channel 2 and use scope in XY mode to see the input versus output.
Remember transistors are current amplifiers but are also non-linear with voltage, current, temperature. A current source ideally is independent of voltage but leakage in CE will make that have a VI slope on the Collector emitter response curve.
So if you want to generate a base current, use a high enough resistance from a voltage source minus Vbe offset to estimate current, so your voltage source is approximately a current source. "Curve tracers" use actual current sources instead for more accuracy. But this simple approach will give you the idea. The load resistance on the output or "Load line" slope is used to determine the operating point on the VI output response. rather than Vin vs I out, use Vout-Iout for this.. But to see gain.. use I out over I in to get hFE or Beta or current gain ( synonyms)
in the example above with the XY mode of scope . use a unipolar signal to sweep the input voltage . any shape sine or triangle 50 to 200Hz will do say 100mV p-p biased at 0.65V on the base thru say a 1K resistor for a starting point.. Observe maximum base current and collector current limits with suitable collector resistor for voltage applied.
added: using 1K base resistor with 1mA input would require 1.65V approx zero to peak voltage on the generator. Zero current would be < 0.6V on Vbe. so your generator should set with aDC offset and signal going from 0.55 say to 1.65 to generate 0 to 1mA input.. Then carefully adjust gain and offset so Vbe never goes negative. to increase base current. More sophisticated sweep source can be made with a current source by design, but for starters, that will allow you see the characteristics.Then using a decade resistor box for collector can change the load line curve. Emitter current sensor can be chosen for range desired like 10 Ω would be 10mV/mA for X axis current. Then adjust scope horizontal gain with that channel gain and offset. for NPN set the null point to the bottom left corner. for PNP set to upper left corner which is inverted polarity.