no, acid does NOT raise TA. Baking soda and washing soda do. The former is familiar but sold by pool stores as "TA Increaser". The latter is less well known but is sold in the laundry section of supermarkets. It too is sold by pool stores as "pH Up!" or "Balance Pak 200" at inflated prices.
TA WILL rise if you add Borax to raise pH, but that's a function of measurement: TA reads higher at higher pH levels.

The only way to increase pH without increase the TA reading is by aeration.

Carl