Measure the DCR of the primary, then double it. This uses the assumption that the secondary uses proportionally sized wire. This resistance is what causes the transformer to have worse regulation, and therefore suggests a practical current limit. For a 10% regulation, use 10% of the mains voltage, i.e., 12V, then Ohm's law to get Imax = (12V) / (2*(pri DCR)).
It could also be 240V or more (typical for an industrial control transformer -- they're pretty common, and 108V possibly hints at three phase use?). To check this, try connecting half the 108VCT winding to 120V,
using a light bulb or load resistor to limit current. Then measure the voltages. If it's topping out not far above 59V (it may look like 70V or more because of the distorted waveform; a true RMS meter, or oscilloscope, would be ideal here), then it is indeed a 120:108VCT transformer, rated for the above current.
(Note that, because of the above regulation rule, using a transformer at half its rated voltage leaves you with
one quarter the VA capacity -- a huge disadvantage. On the upside, the core runs a whole lot cooler.)
Tim