The Nuclear Level Densities (NLDs) and the $gamma$-ray Strength Functions ($gamma$SFs) of $^{153,155}$Sm have been extracted from (d,p$gamma$) coincidences using the Oslo method. The experimental NLD of $^{153}$Sm is higher than the NLD of $^{155}$Sm, in accordance with microscopic calculations. The $gamma$SFs of $^{153,155}$Sm are in fair agreement with QRPA calculations based on the D1M Gogny interaction. An enhancement is observed in the $gamma$SF for both $^{153,155}$Sm nuclei around 3 MeV in excitation energy and is attributed to the M1 Scissors Resonance (SR). Their integrated strengths were found to be in the range 1.3 - 2.1 and 4.4 - 6.4 $mu^{2}_{N}$ for $^{153}$Sm and $^{155}$Sm, respectively. The strength of the SR for $^{155}$Sm is comparable to those for deformed even-even Sm isotopes from nuclear resonance fluorescence measurements, while that of $^{153}$Sm is lower than expected.