Likely not, if it has a "magnetic" ballast typical of a old T12 fixture. I believe the strike voltage (point where gas ionizes and electric arc within the tube start the glow) for a T8 is higher than that of a T12. Magnetic ballasts for T12 won't reach the voltage level needed for a T8.
You can try it. If the ballast is insufficient it will either not light or flicker badly.
Depending on the length, you can still find T12 tubes of 5,000K to 6,700K in home improvement stores' lighting sections.
The original T8 bulbs were substituted directly for T12 bulbs, for power savings. I used to use a DIY light with T8 bulbs and a magnetic ballast, and it worked fine, except when the temperature dropped below about 65F, as I recall, then the bulbs wouldn't light. At normal 70F+ room temperature, it worked fine, discounting the flicker and hum.