That would not be possible as ARIMA assumes that the error term follows white noise process. Therefore, EViews does not have build-in Student's t or GED option like ARCH/GARCH to estimate ARIMA.

As Akram Shavkatovich Hasanov said. No, Eviews does not allow that for ARIMA, you can try other software like R; or you can use Eviews for ARIMA with GARCH.

you can see this video

https://www.youtube.com/watch?v=6N5vvyxxREA

When asked questions such as this by colleagues my initial reaction would be to ask for more details of the series. Did the user look at the background of the series to see if there was any reasons why there might be discontinuities in the series (changes in method of calculation of data, changes in government policy or other interventions). Was there a deterministic element in the series that should have been removed before ARIMA estimation? Perhaps some transformation of the data might help, Perhaps the heavy tails were caused by an ARCH/GARCH effect.

Note that estimates of an AR(p) process are robust with respect to non-normality.

There also appears to be some confusion in earlier answers to this question. To me white noise is a process that is identically distributed with zero mean, constant variance and is uncorrelated. Independent white noise is a process that is independent identically distributed with zero mean and constant variance. Normal white noise is a white noise that follows a normal distribution.

Some of the proposals in the first paragraph should cure your problem. If they do not I would fear that the heavy tails would make you confidence intervals large and you might have to search for an alternative forecasting methodology.