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We examine the charged boson and right-handed neutrino contribution to the muon <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>g</mi><mo>−</mo><mn>2</mn></mrow></semantics></math></inline-formula> anomaly in twin Higgs models with joint constraints of Higgs global fit data, precision electroweak data, leptonic flavor-changing decay <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>μ</mi><mo>→</mo><mi>e</mi><mi>γ</mi></mrow></semantics></math></inline-formula>, and the mass requirement of heavy-gauge bosons. It comes with the conclusion that some parameters, such as the coupling of charged Higgs to the lepton <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>y</mi><mi>μ</mi></msub></semantics></math></inline-formula>, the top Yukawa <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>y</mi><mi>t</mi></msub></semantics></math></inline-formula>, and heavy-gauge boson coupling to the lepton <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>V</mi><mi>μ</mi></msub></semantics></math></inline-formula> are constrained roughly in the range of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0.12</mn><mo>≲</mo><msub><mi>y</mi><mi>μ</mi></msub><mo>≲</mo><mn>0.4</mn></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0.4</mn><mo>≲</mo><msub><mi>y</mi><mi>t</mi></msub><mo>≲</mo><mn>0.9</mn></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0.47</mn><mo>≲</mo><msub><mi>V</mi><mi>μ</mi></msub><mo>≲</mo><mn>1</mn></mrow></semantics></math></inline-formula>, respectively.