Rx and Tx digital signal path latency depends on the configuration of the IC, i.e. interpolation, decimation and the number of taps used in the digital filters.
Rx path is comprised of three half band filter and one programmable FIR filter. Tx path is similarly made up of three half band filters and a programmable FIR filter. Typically the programmable filters have the slowest clocks and the highest number of taps so they dominate the latency.
Delay for each of these filters can be calculated using the formula below:
time delay = N/2 * 1/fs
N - number of taps
fs - filter output sampling frequency.
In a typical application like LTE 10MHz Rx digital latency is 2.23us.
More detail can be found in the AD9361 documentation - Filter Guide section of the Reference Manual.