Strong Rashba effects at surfaces and interfaces have attracted great attention for basic scientific exploration and practical applications. Here, the first-principles investigation shows that giant and tunable Rashba effects can be achieved in KTaO$_3$ (KTO) ultrathin films by applying biaxial stress. When increasing the in-plane compressive strain nearly to -5%, the Rashba spin splitting energy reaches $E_{R}=140$ meV, approximately corresponding to the Rashba coupling constant $alpha_{R}=1.3$ eV {AA}. We investigate its strain-dependent crystal structures, energy bands, and related properties, and thereby elucidate the mechanism for the giant Rashba effects. Furthermore, we show that giant Rashba spin splitting can be kept in the presence of SrTiO$_3$ capping layer and/or Si substrate, and strong circular photogalvanic effect can be achieved to generate spin-polarized currents in the KTO thin films or related heterostructures, which are promising for future spintronic and optoelectronic applications.